Question

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

Answer 1

x = 3.6 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 in the top right, so the side on the bottom left is the hypotenuse.

We know the angle in the lower right corner (angle S), so the side touching it (side ST) with unknown length is the adjacent side. (notice that the points that form the side include the vertex of the angle -- so, it's the adjacent side).

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

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

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

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

`cos(69^o)=(x)/(10)`

To isolate "x", multiply both sides by 10...

`10*cos(69^o)=x`

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

`10*(0.3583679495453...)=x`

`x=3.583679495453...` units

Rounded to the nearest tenth...

x = 3.6 units