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