Question

Find the sine, cosine, and tangent of acute angles A and B in each of the following right triangles. Leave answers in fractional form. a=3,b=4 b=9,c=15 b=20,c=29

Answer 1

In each right triangle, we can find the sine, cosine, and tangent of the given acute angles using ratios of the sides.

Step-by-step explanation:

In each of the given right triangles, we can find the sine, cosine, and tangent of the acute angles A and B using the ratios of the sides. Let's calculate:

Triangle 1: a=3, b=4

• Sine of angle A: sin(A) = opposite/hypotenuse = 3/5 = 3/5
• Cosine of angle A: cos(A) = adjacent/hypotenuse = 4/5 = 4/5
• Tangent of angle A: tan(A) = opposite/adjacent = 3/4 = 3/4
• Sine of angle B: sin(B) = opposite/hypotenuse = 4/5 = 4/5
• Cosine of angle B: cos(B) = adjacent/hypotenuse = 3/5 = 3/5
• Tangent of angle B: tan(B) = opposite/adjacent = 4/3 = 4/3

Similarly, we can calculate for the other right triangles:

• b=9, c=15: sin(A) = 9/15, cos(A) = 12/15, tan(A) = 9/12, sin(B) = 12/15, cos(B) = 9/15, tan(B) = 12/9
• b=20, c=29: sin(A) = 20/29, cos(A) = 21/29, tan(A) = 20/21, sin(B) = 21/29, cos(B) = 20/29, tan(B) = 21/20