Question

Answer all 3 with steps

Answer 1

4. 24.39°

5. 27.29°

6. 38.21°

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=(AB)/(BC) \\\sin C =(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 = (QR)/(QP)\\\tan P = (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 = (XZ)/(YZ)\\\cos Z = (11)/(14)\\\cos Z = 0.7857\\\angle Z= \cos^(-1)(0.7857)\\\angle Z= 38.21\°`