Could you please write the answers clearly and understandably? Thank you. **Problem Description:**A steep mountain is inclined at an angle of 74° to the horizontal and rises $ h = 3600 $ ft above the surrounding plain. A cable car is to be installed from a point $ d = 900 $ ft from the base to the top of the mountain, as shown in the diagram. Determine the shortest length of cable needed. Round your answer to the nearest foot.**Diagram Explanation:**- The diagram includes a mountain with a right triangle formed by the horizontal base, the incline of the mountain, and the vertical rise.- The angle of inclination from the horizontal to the incline of the mountain is 74°.- The vertical rise of the mountain is labeled as $ h = 3600 $ ft.- A point on the horizontal base is marked $ d = 900 $ ft away from the point directly beneath the mountain's peak.- The red line represents the cable from the horizontal point to the top of the mountain, forming the hypotenuse of the triangle.**Solution Steps:**To find the shortest length of cable (hypotenuse), apply trigonometric principles or Pythagorean theorem to the triangle.**Need Help?**- **Read It** for additional explanations.- **Watch It** for a visual walkthrough of the problem-solving process.

Answered: Image /qna-images/answer/a3496347-c413-491e-afd6-39f24cf42fed.jpg

A steep mountain is inclined 74° to the horizontal and rises h = 3600 ft above the surrounding plain. A cable car is to be installed from a point d = 900 ft from the base to the top of the mountain, as shown. Find the shortest length of cable needed. (Round your answer to the nearest foot.) ft

A steep mountain is inclined 74° to the horizontal and rises h = 3600 ft above the surrounding plain. A cable car is to be installed from a point d = 900 ft from the base to the top of the mountain, as shown. Find the shortest length of cable needed. (Round your answer to the nearest foot.) ft

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

Could you please write the answers clearly and understandably? Thank you.

**Problem Description:**

A steep mountain is inclined at an angle of 74° to the horizontal and rises $ h = 3600 $ ft above the surrounding plain. A cable car is to be installed from a point $ d = 900 $ ft from the base to the top of the mountain, as shown in the diagram. Determine the shortest length of cable needed. Round your answer to the nearest foot.

**Diagram Explanation:**

- The diagram includes a mountain with a right triangle formed by the horizontal base, the incline of the mountain, and the vertical rise.
- The angle of inclination from the horizontal to the incline of the mountain is 74°.
- The vertical rise of the mountain is labeled as $ h = 3600 $ ft.
- A point on the horizontal base is marked $ d = 900 $ ft away from the point directly beneath the mountain's peak.
- The red line represents the cable from the horizontal point to the top of the mountain, forming the hypotenuse of the triangle.

**Solution Steps:**

To find the shortest length of cable (hypotenuse), apply trigonometric principles or Pythagorean theorem to the triangle.

**Need Help?**

- **Read It** for additional explanations.
- **Watch It** for a visual walkthrough of the problem-solving process.

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