What is the length of Line segment A B? Round to the nearest tenth. Triangle A B C is shown. Angle A C B is a right angle and angle C A B is 75 degrees. The length of C A is 10 meters and the length of hypotenuse A B is x. 9.7 m 10.4 m 37.3 m 38.6 m

AB = 38.6metres

Step-by-step explanation:

Given the right angled triangle ABC with hypotenuse AB and ∠CAB to be 75°, the opposite side of the triangle will be the side facing the angle ∠CAB directly and this is side BC. The adjacent side of the triangle will be side CA.

To get the length of the hypotenuse AB, we will use the trigonometry identity SOH, CAH, TOA.

According to CAH;

Cos∠CAB = adjacent/hypotenuse = CA/AB

Substituting CA = 10 metres and ∠CAB = 75° into the equation;

Cos75° = 10/AB

AB = 10/cos75°

AB = 10/0.2588

AB = 38.6metres

Hence the length of the hypotenuse AB is 38.6metres.

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