In ΔTUV, the measure of ∠V=90°, VT = 64 feet, and UV = 43 feet. Find the measure of ∠U to the nearest tenth of a degree.

Question

Mathematics

Elias

12 April, 02:29

In ΔTUV, the measure of ∠V=90°, VT = 64 feet, and UV = 43 feet. Find the measure of ∠U to the nearest tenth of a degree.

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Kennedi · Answer 1

47.8°

Step-by-step explanation:

Let's first outline the important parameters

-- -
Vt = 64

UV = 43

The angles in a triangle sums up to 180, but we don't have up to 2 angles given so as to find the third one. What we have to is to find the second angle, in this case T, using the sine rule.

Sin v/v = sin t/t

(Sin 90) / 64 = sin t/43

Cross multiply and we have

43 sin 90 = 64 sin t

Sin t = 43 sin 90 : 64

Sin t = 0.6719

Sine inverse of t = 42.2° (the second angle)

Angle U = 180 - (90 + 42.2)

180 - 132.2

= 47.8°