Question

Solve the right trianglw. Round decimal answers to the nearest tenth.

Answer 1

(1) To find X

using trigonometry function. opposite = 18, Hypotaneus = 25

Then using:

`\begin{gathered} \sin \theta\text{ = }\frac{OP\P}{\text{ADJ}} \\ \sin \theta\text{ =}(18)/(25) \\ s\text{in}\theta=0.72\text{ } \\ \theta=sin^(-1)(0.72) \\ \theta\text{ = }46.05^(\cdot) \end{gathered}`

(2) To find Z,

X + Z + 90 = 180 (sum of angle in a triangle)

46.05 + Z +90 = 180

136.05 + z = 180

Z = 180 - 136.05

Z = 43.94 degrees

(3) To find XY, by using Pythagoras Theorem, we have.

`\begin{gathered} (Hyp)^2=(Opp)^2+(Adj)^2 \\ 25^2=18^2+XY^2 \\ 625=324+XY^2 \\ 301=XY^2 \\ XY^2\text{ = 301} \\ XY\text{ = }\sqrt[]{301} \\ XY\text{ = 17.34} \end{gathered}`