Question

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.

Answer 1

U=56.1038≈56.1

Explanation:

tanU=

adjacent

opposite

​

=

43

64

​

\tan U = \frac{64}{43}

tanU=

43

64

​

U=\tan^{-1}(\frac{64}{43})

U=tan

−1

(

43

64

​

)

U=56.1038\approx 56.1^{\circ}

U=56.1038≈56.1

∘

Answer 2

47.8°

Explanation:

Let's first outline the important parameters

--- <V = 90°

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°