Math Problem Statement

Use the trig functions to find the missing side lengths. Round to the nearest hundredth. Use the trig functions to find the value of θ. Round to the nearest degree.

Solution

Let me analyze the image and extract the mathematical problems for solving. One moment, please!The image contains problems based on trigonometric functions, including finding missing angles and sides in right triangles using sine, cosine, and tangent. Below is the breakdown of the tasks:

1. Tasks on Finding the Angle (θ):

You are asked to use trigonometric functions to find the value of the angle θ\theta, rounding to the nearest degree. Examples include:

  • cosθ=45\cos \theta = \frac{4}{5}
  • sinθ=37\sin \theta = \frac{3}{7}
  • tanθ=2017\tan \theta = \frac{20}{17}

2. Tasks on Finding Missing Side Lengths:

You are asked to use trigonometric functions to find the missing side length, rounding to the nearest hundredth. Examples include:

  • \triangle with known sides like 39 and 26.
  • \triangle with hypotenuse and one leg given (e.g., 34 and 27).

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sine
Cosine
Tangent
Triangle Geometry

Formulas

sin(θ) = Opposite / Hypotenuse
cos(θ) = Adjacent / Hypotenuse
tan(θ) = Opposite / Adjacent

Theorems

Pythagorean Theorem
Basic Trigonometric Identities

Suitable Grade Level

Grades 9-11