The side opposite to the 90 degree angle is called the hypotenuse in the right-angled triangle.\u00a0<\/span><\/p>\n Here in this triangle,<\/span><\/p>\n a \u2013 perpendicular (the side opposite to \u019f)<\/span><\/p>\n b \u2013 base<\/span><\/p>\n c – hypotenuse<\/span><\/p>\n The trigonometric ratio sine (sin) is simply the ratio of the side opposite the angle to the hypotenuse and can be written as:<\/span><\/p>\n Sin \u019f = Perpendicular \/ Hypotenuse<\/span><\/p>\n So here Sin \u019f = a \/ c<\/span><\/p>\n There are 6 trigonometric ratios namely <\/span>sin, cos, tan, cosec, sec and cot<\/i><\/b>. See the table below to find the values of these ratios and also their reciprocals.<\/span><\/p>\n \u00a0<\/span><\/p>\n As can be seen, cosec is simply the reciprocal of sin as the formula to find cosec is the reciprocal of sin.\u00a0<\/span><\/p>\n Though these ratios can be calculated for all angles, there are some standard examples such as 0\u00b0, 30\u00b0, 45\u00b0, 60\u00b0 and 90\u00b0. These ratios can also be written in terms of \u03c0 which here is interpreted as 180\u00b0 angle. The table below shows the value of these standard angles:<\/span><\/p>\n <\/span><\/p>\n \u00a0<\/span><\/p>\n The table shows that the value of sin 30\u00b0 is \u00bd or 0.5.<\/i><\/b><\/p>\n <\/i><\/b><\/p>\n There are two methods of deriving sin 30\u00b0. Let us see both the methods below:<\/span><\/p>\n Method 1<\/b>: Let\u2019s take an equilateral triangle. An equilateral triangle has all the angles equal to 60\u00b0 and all sides are also equal.\u00a0<\/span><\/p>\n Step 1<\/i><\/b>. Draw a line perpendicular to the side BC. Also, since it is an equilateral triangle, let the length of the sides be \u20182a\u2019 so AB = BC = AC = 2a.<\/span><\/p>\n Step 2<\/i><\/b>. The perpendicular divides the side BC into half thus making BD= DC = a and also bisects the angle at A making it 30\u00b0.<\/span><\/p>\n The triangle ABD is a right-angled triangle at D.<\/span><\/p>\n Sin 30\u00b0 = Side opposite to the angle 30\u00b0\/ Hypotenuse\u00a0<\/span><\/p>\n Sin 30\u00b0 = BD\/ AB<\/span><\/p>\n Sin 30\u00b0 = a\/2a = \u00bd or 0.5<\/span><\/p>\n Hence, the value of Sin 30\u00b0= \u00bd.<\/span><\/p>\n Method 2<\/b>: The value can be derived by construction as well.\u00a0<\/span><\/p>\n Step 1<\/i><\/b>. Draw a straight line from a point P. Use a protractor and ruler to draw a 30\u00b0 angle from point P.\u00a0<\/span><\/p>\n Step 2<\/i><\/b>. Since we need to know the lengths so use the compass and set the length as 6 cm. This point will come out to be Q.<\/span><\/p>\n Step 3<\/i><\/b>. Draw a line perpendicular to the original horizontal line and mark the point R on where it intersects the original line. When you use a ruler to measure the length of QR, you will find the value as 3 cm.\u00a0<\/span><\/p>\n So,\u00a0<\/span><\/p>\n Sin 30\u00b0 = Perpendicular or side opposite the angle \/ Hypotenuse<\/span><\/p>\n Sin 30\u00b0 = 3 \/ 6<\/span><\/p>\n Sin 30\u00b0 = \u00bd<\/span><\/p>\n The law of sine (sin) becomes helpful when we solve triangles.\u00a0 The law states that the sides of any triangle are in proportion to the sine of the opposite angles. The law can be written as:<\/span><\/p>\n a\/ Sin A = b\/ Sin B = c\/ Sin C<\/span><\/p>\n Where a, b and c are sides with angles A, B and C opposite to each other.\u00a0\u00a0<\/span><\/p>\n This law is useful in two scenarios. Firstly, when we know two angles and one side and secondly, two sides and a non-included angle which is an angle that doesn\u2019t lie between the sides.\u00a0<\/span><\/p>\n For example:<\/strong> Given a triangle PQR with two angles as 30\u00b0 and 60\u00b0 and the length of one side as 7 cm.\u00a0<\/span><\/p>\n We have to find the value of p.<\/span><\/p>\n Putting all the values we know,\u00a0<\/span><\/p>\n p\/ Sin P = q\/ Sin Q = r\/ Sin R<\/span><\/p>\n p\/ Sin 30\u00b0 = 7\/ Sin 90\u00b0 = r\/ Sin 60\u00b0<\/span><\/p>\n p\/(1\/2) = 7\/ 1 = r\/ \u221a3<\/span><\/p>\n (Since the sum of all angles of a triangle is 180\u00b0 so angle Q = 180\u00b0 – (60\u00b0 + 30\u00b0) = 90\u00b0<\/span><\/p>\n Using algebra,\u00a0 we get<\/span><\/p>\n \u00a0p = 7\/2<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.9.11″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”http:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” module_class=”img1″ _builder_version=”4.9.10″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/sin-90.png\")
<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-0-01-300x140.png\")
<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Sin-0-02-300x118.png\")
\u00a0<\/span><\/p>\nDERIVATION OF SIN 30\u00b0<\/b><\/h3>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/sin30_1-300x215.png\")
\u00a0<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/sin30_2-300x209.png\")
<\/span><\/p>\nTHE LAW OF SINE<\/b><\/h3>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/sin30_3-300x135.png\")
<\/span><\/p>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n