Question

Find the angle measure indicated to the nearest tenth:

Answer 1

Step-by-step explanation:

Sin<D = Opposite / Hypotenuse

Opposite - EC

Hyp - DE

Sin<D = EC/DE = x/9

we need x to find <D.

so -->Use pythagorean theorem.

DE^2 = EC^2 + DC^2

DE = 9 DC = 7 EC = ?

EC^2 = DE^2 - DC^2 rearranged.

= 9^2 - 7^2

= 81 - 49

EC^2 = 32 Put both sides under square root.

√(EC^2) = √32

EC = 4√2 ~ 5.65.

We now have X which was representing the unknown side EC.

Sin<D = EC/DE = 5.65/9 = 0.627

To find <D Take the sine inverse of of 0.627.

<D = Arcsin(0.627) = 38.82°.

We now know <D. It's <E's turn.

A right angle triangle has a summation of interior angles of 180°.

thus, <D + <C + <E = 180°

38.82° + 90° + <E = 180°

128.82° + <E = 180°

subtract both sides by 128.82°

0 + <E = 180° - 128.82°

<E = 51.2°