A right triangle has side lengths AC=7inches,BC=24 inches, and AB=25inches What are the measures of the angles in triangle ABC? mangle Aapprox 46.2^circ ,mangle Bapprox 43.8^circ ,mangle Capprox 90^circ mangle Aapprox 73.0^circ ,mangle Bapprox 17.0^circ ,mangle Capprox 90^circ mangle Aapprox 73.7^circ ,mangle Bapprox 16.3^circ ,mangle Capprox 90^circ mangle Aapprox 74.4^circ ,mangle Bapprox 15.6^circ ,mangle Capprox 90^circ

Question

A right triangle has side lengths AC=7inches,BC=24 inches, and AB=25inches What are the measures of the angles in triangle ABC? mangle Aapprox 46.2^circ ,mangle Bapprox 43.8^circ ,mangle Capprox 90^circ mangle Aapprox 73.0^circ ,mangle Bapprox 17.0^circ ,mangle Capprox 90^circ mangle Aapprox 73.7^circ ,mangle Bapprox 16.3^circ ,mangle Capprox 90^circ mangle Aapprox 74.4^circ ,mangle Bapprox 15.6^circ ,mangle Capprox 90^circ

Answer 1

To find the measures of the angles in triangle ABC, we can use the trigonometric ratios sine, cosine, and tangent.Step 1: Calculate the sine of angle A using the formula:sin(A) = opposite/hypotenusesin(A) = BC/ABsin(A) = 24/25sin(A) ≈ 0.96Step 2: Calculate the cosine of angle A using the formula:cos(A) = adjacent/hypotenusecos(A) = AC/ABcos(A) = 7/25cos(A) ≈ 0.28Step 3: Calculate the tangent of angle A using the formula:tan(A) = opposite/adjacenttan(A) = BC/ACtan(A) = 24/7tan(A) ≈ 3.43Step 4: Calculate the measure of angle A using the inverse tangent function:A = tan^(-1)(tan(A))A ≈ tan^(-1)(3.43)A ≈ 73.7°Step 5: Calculate the measure of angle B using the fact that the sum of the angles in a triangle is 180°:B = 180° - A - CB = 180° - 73.7° - 90°B ≈ 16.3°Step 6: Calculate the measure of angle C using the fact that the sum of the angles in a triangle is 180°:C = 180° - A - BC = 180° - 73.7° - 16.3°C ≈ 90°Therefore, the measures of the angles in triangle ABC are:

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