Find the value of each variable. Round the answer to the nearest tenth. **Find the value of each variable. Round your answers to the nearest tenth.**---**Problem 36:**- Triangle diagram with the following details: - One side is labeled as $ 9 $. - The side opposite to the angle of $ 56^\circ $ is labeled as $ a $. - The side adjacent to the angle of $ 56^\circ $ opposite to the right angle is labeled as $ b $. - There is a right angle between side $ 9 $ and side $ b $.---**Problem 37:**- Triangle diagram with the following details: - One side is labeled as $ 7.7 $. - The side opposite to the angle of $ 67^\circ $ is labeled as $ d $. - The side adjacent to the angle of $ 67^\circ $ opposite to the right angle is labeled as $ c $. - There is a right angle between side $ 7.7 $ and side $ c $.---**Instruction:** To solve these problems, use trigonometric ratios (sine, cosine, and tangent) for right triangles. Calculate the unknown sides, and round your answers to the nearest tenth. Make use of the following formulas where necessary:- For a given angle $ \theta $: - $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$ - $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$

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Description: Find the value of each variable. Round the answer to the nearest tenth. **Find the value of each variable. Round your answers to the nearest tenth.**---**Problem 36:**- Triangle diagram with the following details: - One side is labeled as $ 9 $.

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Math

Geometry

Find the value of each variable. Round your answers to the nearest tenth. 36. b 37. 7.7 56 67

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

Find the value of each variable. Round the answer to the nearest tenth.

**Find the value of each variable. Round your answers to the nearest tenth.**

---

**Problem 36:**
- Triangle diagram with the following details:
- One side is labeled as $ 9 $.
- The side opposite to the angle of $ 56^\circ $ is labeled as $ a $.
- The side adjacent to the angle of $ 56^\circ $ opposite to the right angle is labeled as $ b $.
- There is a right angle between side $ 9 $ and side $ b $.

---

**Problem 37:**
- Triangle diagram with the following details:
- One side is labeled as $ 7.7 $.
- The side opposite to the angle of $ 67^\circ $ is labeled as $ d $.
- The side adjacent to the angle of $ 67^\circ $ opposite to the right angle is labeled as $ c $.
- There is a right angle between side $ 7.7 $ and side $ c $.

---

**Instruction:**

To solve these problems, use trigonometric ratios (sine, cosine, and tangent) for right triangles. Calculate the unknown sides, and round your answers to the nearest tenth. Make use of the following formulas where necessary:

- For a given angle $ \theta $:
- $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$
- $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$
- $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$

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