In triangle ABC, angle C is straight, AC = 9, cos A = 0.3. Find AB.

In the statement of the problem it is said that the angle C is a straight line.

According to the definition of a right-angled triangle, triangle ABC is right-angled.

Right-angled triangle – a triangle in which one corner is a straight line (equal to 90 degrees).

So side AC is a leg of a right-angled triangle ABC;

AB is the hypotenuse of the right-angled triangle ABC.

The formula for finding the cosine of an angle in a right triangle
Let’s remember what is the cosine of an acute angle in a right triangle and write down the corresponding ratio for a right triangle ABC.

The cosine of an acute angle of a right triangle is the ratio of the adjacent leg to the hypotenuse.

For our triangle it looks like:

cos A = AC / AB.

Let us express the hypotenuse AB from this equality.

AB is the unknown divisor in this equality.

According to the rule, to find an unknown divisor, the dividend must be divided by the quotient.

AB = AC / cos A;

Substitute the given values ​​and perform calculations.

AB = 9 / 0.3 = 9: 3/10 = 9 * 10/3 = 3 * 10 = 30 units.

So, the length of the hypotenuse is found and it is equal to 30 units.

Answer: the length of the hypotenuse AB = 30 units.

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