the value of x is 9 â answer b
step-by-step explanation:
* we can solve this problem using cosine and sine rule
- in δ abc
âľ ab = 36 , bc = 28 , ac = 16
- lets find the measure of angle b using the cosine rule
⾠cos b = [ab² + bc² - ac²]/2(ab)(bc)
ⴠcos b = [36² + 28² - 16²]/2(36)(28)
â´ cos b = 19/21
â´ mâ b = cos^-1(19/21) â
25°
- lets find the measure of angle a using the sine rule
âľ sina/bc = sinb/ac = sinc/ab
â´ sina/28 = sin25°/16 â by using cross multiplication
ⴠsina = 28 à sin25°/16
â´ sina = 0.7396
â´ mâ a = sin^-1(0.7396) â
48°
- from the figure mâ abd = mâ dbc
âľ mâ abc = 25°
â´ mâ abd = 25°/2 = 12.5°
- in δabd
âľ mâ a = 48° , mâ abd = 12.5°
⾠the sum of the measures of the interior angles of any δ is 180°
â´ mâ adb = 180° - (48° + 12.5°) = 119.5°
âľ ab = 36
âľ ad = x
- use the sine rule to find x
âľ sinâ adb/ab = sinâ abd/x
â´ sin119.5°/36 = sin12.5°/x â by using cross multiplication
â´ x = 36 Ă sin12.5°/sin119.5° = 8.95 â
9
* the value of x is 9