Question

Solve for x. Round to the nearest tenth, if necessary.

Answer 1

x=15.4 units

Explanation:

First, some definitions before working the problem:

The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:

`sin(\theta)=(opposite)/(hypotenuse)`

`cos(\theta)=(adjacent)/(hypotenuse)`

`tan(\theta)=(opposite)/(adjacent)`

One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.

The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.

Working the problem

For the given triangle, the right angle is at the bottom, so the side on top is the hypotenuse. We know the angle in the upper right corner, so the side across from it with length 4.5, is the opposite side.

For this triangle, the "opposite" leg is known. Additionally, the "hypotenuse" is unknown and is our "goal to find" side.

Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".

Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh". So, the desired function to use for this triangle is the Sine function.

`sin(\theta)=(opposite)/(hypotenuse)`

`sin(17^o)=(4.5)/(x)`

Multiply both sides by x, and divide both sides by sin(17°)...

`x=(4.5)/(sin(17^o))`

Make sure your calculator is set to degree mode, and calculate:

`x=(4.5)/(0.2923717047227...)`

`x=15.391366289249...` units

Rounded to the nearest tenth...

`x=15.4` units