Question

In ΔRST, the measure of ∠T=90°, the measure of ∠R=64°, and RS = 5.8 feet. Find the length of ST to the nearest tenth of a foot.

Answer 1

Answer:

The length of ST to the nearest tenth of a foot is 5.2 ft

Step-by-step explanation:

Here we have

∡T = 90°

∡R = 64°

RS = 5.8 ft

To answer the question, we have apply sine rule as follows;

$\frac{a}{Sin\alpha } = \frac{b}{sin\beta } = \frac{c}{sin\gamma}$

Therefore, for triangle RST, we will have;

$\frac{RS}{SinT } = \frac{ST}{sinR } = \frac{RT}{sinS}$

Therefore;

$\frac{5.8}{Sin90 } = \frac{ST}{sin64 }$ from which

${ST}{ } = \frac{5.8 \times sin64}{Sin90 } = 5.213 \, ft$

Therefore, the length of ST to the nearest tenth of a foot = 5.2 ft.