Question

solve the right triangle shown in the figure.
a = 10.6, b = 24

a. what is the length of the side?
c ≈ 26.24 (round to the nearest hundredth as needed.)
b. what are the angles?
a ≈ 23.8 ° (round to the nearest tenth as needed.)
b ≈ □° (round to the nearest tenth as needed.)

Explanation:

Step1: Recall triangle angle sum

In a right triangle, one angle is \(90^\circ\), and the sum of angles is \(180^\circ\). So \(A + B + 90^\circ= 180^\circ\), which simplifies to \(A + B = 90^\circ\).

Step2: Calculate angle B

We know \(A\approx23.8^\circ\), so \(B = 90^\circ - A\). Substitute \(A\): \(B = 90 - 23.8 = 66.2^\circ\).

Answer:

\(B\approx\boxed{66.2}\)