Question

Given the right triangle shown, solve for X, Y and Z. The triangle may not be drawn to scaleA. x=1.86feet, y=4.41 feet and z=65 degreeB.x=4.41 feet, y=1.69 feet, and z=155 degreeC. x=8.58 feet, y=9.46 feet and z=65 degreeD.x=9.46 feet, y=8.58 feet and z=155 degree

Answer 1

Since the triangle is a right-angled triangle, we can use SohCahToa to find x

Using the ratio

`Tan25=\frac{\text{opposite}}{\text{adjacent}}`

Opposite = 4ft

adjacent = x

Substituting these values yield

`\begin{gathered} \text{Tan 25 =}(4)/(x) \\ x\text{ =}(4)/(\tan 25) \\ x\text{ =8.57}8ft \\ x\approx8.58ft \end{gathered}`

To find Z we use the fact that the sum of angles in a triangle is 180 degrees

so that in triangle XYZ

90 + 25 +Z = 180

Z = 180 - 115

Z= 65 degrees

We will now use Pythagoras theorem to find y

`\begin{gathered} \text{For that} \\ y^2=x^2+4^2 \\ \text{but x = 8.58ft} \\ y^2=8.58^2+4^2 \\ y=\sqrt[]{73.6164\text{ +16}} \\ y\text{ =9.46 ft} \end{gathered}`

Hence x= 8.58 ft, y= 9.46ft and Z = 65 degrees, Option C