Question

for the triangle shown below, find a if ∠a = 53° and b = 15. (round your answer to the nearest tenth.) 20.1 19.7 19.3 19.5 19.9

Explanation:

Step1: Use tangent function

In right - triangle \(ABC\), \(\tan A=\frac{a}{b}\).

Step2: Substitute given values

Given \(A = 53^{\circ}\) and \(b = 15\), so \(a=b\times\tan A=15\times\tan(53^{\circ})\).
We know that \(\tan(53^{\circ})\approx1.3270\). Then \(a = 15\times1.3270=19.905\).

Step3: Round the result

Rounding \(19.905\) to the nearest tenth gives \(19.9\).

Answer:

19.9