Math Problem Statement

حساب ab

حساب ab

Solution

The diagram you provided shows a right triangle with one angle marked as 73°, a right angle at point A, and a length of 22 for one side (most likely the adjacent side to the 73° angle). Let's proceed to find the length of side ABAB, which I assume is the hypotenuse.

We can use trigonometric relationships, specifically the cosine function, since we have the adjacent side (22) and the angle (73°). The cosine function is defined as:

cos(θ)=adjacenthypotenuse\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}

In this case: cos(73)=22AB\cos(73^\circ) = \frac{22}{AB}

We can solve for ABAB:

AB=22cos(73)AB = \frac{22}{\cos(73^\circ)}

Let me calculate that for you.The length of side ABAB (the hypotenuse) is approximately 75.25 units.

Do you need further details on this solution, or have any other questions?

Here are 5 related questions to expand on this:

  1. How can you find the length of side ACAC using trigonometric functions?
  2. What is the sine of angle B\angle B in this triangle?
  3. Can you verify the area of this triangle using the calculated hypotenuse?
  4. How would you solve this triangle if the angle given were different?
  5. What is the value of angle CC in this triangle?

Tip: Always remember to check if you're working with degrees or radians when using trigonometric functions!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangle Properties

Formulas

cos(θ) = adjacent/hypotenuse

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-12