Question

Suppose ABC is a right triangle with sides​ a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the values of the six trigonometric functions for angle B.

Answer 1

a =
`√(7)`

Explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.:

Suppose ABC is a right triangle with sides​ a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the values of the six trigonometric functions for angle B. when b=3 and c=4.

My answer:

We will Pythagoras theorem, which states that the sum of squares of two legs of a right triangle is equal to the square of the hypotenuse of right triangle. Because the question says that ABC is a right triangle.

`a^2+b^2=c^2`

Given that: b=3 and c=4

`a^2+3^2=4^2a^2+9=16a^2+9-9=16-9a^2=7`

so a =
`√(7)`

We know that tangent relates opposite side of a right triangle with adjacent side.

`\text{tan}(B)=(a)/(b)\\\text{tan}(B)=(√(7))/(3)`

Please have a look at the attached photos.