Question

Which angle has a tangent value of 7/24 ?

∠A

∠C

∠B

Answer 1

The question does not provide enough details but the angle with a tangent of 7/24 can be found by using the inverse tangent function on a calculator.

Step-by-step explanation:

The student is asking for the angle which has a tangent value of 7/24. Remembering that the tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side, we look for an angle whose corresponding sides have lengths in the ratio of 7:24. This question does not provide enough context or data about angles ∠A, ∠B, and ∠C to determine which angle has a tangent of 7/24 without additional information or calculation. However, if we had a right triangle where one of the angles yielded a tangent value of 7/24, we would use the inverse tangent function (arctan) on a calculator to find the measure of that angle. The inverse tangent of 7/24 would give us the measure of the angle in question.

Answer 2

Answer: Angle A

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Step-by-step explanation:

x = length of segment BC

Use the pythagorean theorem to find that

a^2+b^2 = c^2

x^2+24^2 = 25^2

x^2+576 = 625

x^2 = 625-576

x^2 = 49

x = sqrt(49)

x = 7

Segment BC is 7 units.

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The tangent of an angle is equal to the ratio of the opposite over adjacent.

In terms of an equation,

tan(angle) = opposite/adjacent

Replace "opposite/adjacent" with 7/24

tan(angle) = 7/24

Note how the 7 matches up with BC and the 24 matches up with BA

This means,

tan(angle) = 7/24 = BC/BA

If angle A is the reference angle, then BC is the opposite side and BA is the adjacent side.

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tan(angle) = opposite/adjacent

tan(A) = BC/BA

tan(A) = 7/24