Math Problem Statement

The image contains multiple geometry problems, mostly focused on right triangles. The specific tasks include finding unknown sides using trigonometric ratios like sine, cosine, and tangent.

Solution

The image you uploaded contains several geometry problems, which appear to involve right triangles. Let's break down the problems:

  1. Problem 10: You have a right triangle with one angle of 64° and a side of length 42. You're asked to find the length of side xx. This can be solved using trigonometric ratios such as sine, cosine, or tangent, depending on the missing information.

  2. Problem 11: Here, you have a right triangle where the angle is 70° and the side opposite to it has a length of 13. You need to find the length of side yy. Again, trigonometric functions will be used.

  3. Problem 12: You are asked to find DCDC in triangle ABCABC, where the right angle is at DD. Side ABAB has a length of 20, and angles are given as 54° and 28°. You can apply the Law of Sines or the Law of Cosines to solve this.

  4. Problem 14: A 30-foot tall telephone pole is connected to the ground with a wire that forms a 48° angle with the pole. You're asked to find the length of the wire. This is another trigonometry problem, which can be solved using the sine or cosine rule.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangles
Law of Sines
Law of Cosines

Formulas

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

Theorems

Law of Sines
Law of Cosines

Suitable Grade Level

Grades 9-12