High School

Tia and Braden are standing 12 feet apart from each other on opposite sides of an in-ground swimming pool. They spot a pair of goggles on the pool floor between them. The angle of depression from Tia to the goggles is 65°, and the angle of depression from Braden to the goggles is 28°. Find the direct distance (to the nearest tenth) from Tia to the goggles.

Answer :

To find the direct distance from Tia to the goggles, we can use trigonometry and the given angles of depression.

Let's denote the distance from Tia to the goggles as "x".

From the given information, we can form a right triangle. Tia's line of sight to the goggles forms one of the acute angles, and the distance between Tia and Braden (12 feet) is the opposite side of that angle.

Using the tangent function, we can set up the following equation:

tan(65°) = opposite side / adjacent side

tan(65°) = x / 12

To solve for x, we can rearrange the equation:

x = tan(65°) * 12

Using a calculator, we can evaluate the expression:

x ≈ 30.58 feet

Therefore, the direct distance from Tia to the goggles is approximately 30.6 feet (rounded to the nearest tenth).

Learn more about tangent function Here-

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