Question

Angles C and D are acute angles of a right triangle. Given sin D=2/7, which statement is true?

Answer 1

Answer

Option D is correct.

Cos C = (2/7)

Explanation

In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

A sketch of this right triangle will be

This sketch allows Sin D = (2/7)

To know the right answer, we need to find the last side of the triangle

The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.

The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.

The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,

a² + b² = (hyp)²

For this question,

a = 2

b = ?

hyp = 7

a² + b² = (hyp)²

2² + b² = 7²

4 + b² = 49

b² = 49 - 4

b² = 45

b = √45

So, we can evaluate each of these

Cos D = (√45)/7

Cos C = (2/7)

Hope this Helps!!!