Question

Trigonometry, find the missing angle!

Answer 1

46

Explanation:

13.3 = H

9.2 = A

AH = cos

cos⁻¹(9.2÷13.3) = 46.23°

Answer 2

`\boxed {\boxed {\sf \angle z \approx 46 \textdegree}}`

Explanation:

First, recall the three trigonometric ratios.

• sin(θ)= opposite/hypotenuse
• cos(θ)= adjacent/hypotenuse
• tan(θ)= opposite/adjacent

13.3 is the hypotenuse because it is opposite the right angle. 9.2 is the adjacent because it is next to angle z. We must use cosine.

• hypotenuse= 13.3

• adjacent= 9.2

First, plug the values into the cosine ratio.

• cos(z)=9.2/13.3

Divide.

• cos(z)=0.691729323

Next, use the inverse of cosine because we are trying to solve for the angle.

• z= cos⁻¹(0.691729323)
• z= 46.23284386

Round to the nearest degree. The 2 in the tenth place tells us to leave the 6 in the ones place.

• z≈46

Angle z is about 46 degrees