Question

Given the following triangle, if b = 9 and B = 15°, find a.

0.27
2.41
33.59

Answer 1

SOH,CAH, TOA so it would be TANGENT since it would be Opposite over Adjacent. Tan(15) = 9/a put Tan(15) onto your calculator it would be .267949 round that to .27 = 9/a cross multiply
a = 33.588. C is the correct answer.

Answer 2

33.59 ( approx )

Explanation:

Since, the sum of all interior angle of a triangle is supplementary,

Thus, for the triangle ABC,

∠A + ∠B + ∠C = 180°

Given, ∠B = 15° and ∠C = 90°,

⇒ ∠A + 15° + 90° = 180° ⇒ ∠A + 105° = 180° ⇒ ∠A = 180° - 105° = 75°,

Now, By the law of sine,

In triangle ABC,

`(sin A)/(a)=(sin B)/(b)`

We have, b = 9 unit,

`\implies (sin 75^(\circ))/(a)=(sin 15^(\circ))/(9)`

`\implies 9* (sin 75^(\circ))/(sin 15^(\circ)) = a`

`\implies 9* 3.73205080757=a\implies a = 33.5884572681\approx 33.59`

Thus, the value of a is 33.59 unit ( approx )