Calculate the missing variables
1. Opposite= h Agecent= 88 hypotenuse = 146 angle= 53 °
2. Opposite= 5.9 Agecent= 3.1 hypotenuse = 4.3 angle= a°
3. Opposite= 21 Agecent= p hypotenuse = 21 angle= 32°


Let's solve these right triangles step by step:

### 1. Opposite \( = h \), Adjacent \( = 88 \), Hypotenuse \( = 146 \), Angle \( = 53^\circ \)
- We'll use trigonometric identities like sine, cosine, and tangent to solve this.

#### Step 1: Find the opposite side \( h \)
Using the sine function:
\[
\sin(53^\circ) = \frac{h}{146}
\]
\[
h = 146 \times \sin(53^\circ)
\]
Calculating \( h \):
\[
h \approx 146 \times 0.7986 \approx 116.1
\]

#### Step 2: Verify the adjacent side
Using the cosine function:
\[
\cos(53^\circ) = \frac{88}{146}
\]
Checking if this holds:
\[
\cos(53^\circ) \approx 0.6018
\]
\[
\frac{88}{146} \approx 0.6027
\]
This is close, confirming the values are correct.

So, \( h \approx 116.1 \).

---

### 2. Opposite \( = 5.9 \), Adjacent \( = 3.1 \), Hypotenuse \( = 4.3 \), Angle \( = a^\circ \)

#### Step 1: Find the angle \( a^\

Calculate the missing variables
1. Opposite= h, Adjacent= 88, Hypotenuse = 146, Angle= 53°
2. Opposite= 5.9, Adjacent= 3.1, Hypotenuse = 4.3, Angle= a°
3. Opposite= 21, Adjacent= p, Hypotenuse = 21, Angle= 32°

Learn how to calculate the missing variables in right-angle triangles using trigonometric identities. Solve for angles, opposite, adjacent, and hypotenuse values through detailed step-by-step solutions. This problem is ideal for students in Grades 9-12 and involves key concepts in trigonometry.

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