Question

Answer all 3 with steps

Answer 1

Answer:

4. 24.39°

5. 27.29°

6. 38.21°

Step-by-step explanation:

Given:

Δ ABC is right angle at A

Δ PQR is right angle at Q

Δ XYZ is right angle at X

To find:

∠ C = ?

∠ P = ?

∠ Z = ?

Solution:

For 4.)

We Know the Identities,

$\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}$

∴ $\sin C=\frac{AB}{BC} \\\sin C =\frac{19}{46} \\\sin C =0.413\\\therefore C= sin^{-1}(0.413)\\ \angle C=24.39\°$

For 5.)

$\tan P = \frac{\textrm{side opposite to angle P}}{\textrm{side adjacent to angle P}}\\\tan P = \frac{QR}{QP}\\\tan P = \frac{16}{31}\\\tan P = 0.5161\\\angle P=\cos^{-1}(0.5161)\\\angle P=27.29\°$

For 6.)

$\cos Z = \frac{\textrm{side adjacent to angle Z}}{Hypotenuse}\\\cos Z = \frac{XZ}{YZ}\\\cos Z = \frac{11}{14}\\\cos Z = 0.7857\\\angle Z= \cos^{-1}(0.7857)\\\angle Z= 38.21\°$