In triangle ABC, angle C = 90 °, AC = 15cm, BC = 8cm. Find sinA, cosA, tgA, sinB, cosB, tgB

Given:

Right-angled triangle ABC;

Angle C – 90 degrees;

AC = 15 cm;

BC = 8 cm;

Find: sin A, cos A, tg A, sin B, cos B, tg B.

Decision:

In triangle ABC, angle C is 90 degrees.

AB – hypotenuse;

AC, BC – hypotenuse.

According to the Pythagorean formula:

AB ^ 2 = AC ^ 2 + BC ^ 2;

Find AB:

AB = √ (AC ^ 2 + BC ^ 2) = √ ((15 cm) ^ 2 + (8 cm) ^ 2) = √ (225 cm ^ 2 + 64 cm ^ 2) = √ (289 cm ^ 2) = 17 cm.

Find the corners:

sin A = AC / AB = 15/17;

cos A = BC / AB = 8/17;

tg A = AC / BC = 15/8;

sin B = BC / AB = 8/17;

cos B = AC / AB = 15/17;

tg B = BC / AC = 8/17.