Question

Determine the unknown measures of the triangle shown. Round to the nearest tenth, if necessary

Answer 1

x = 25

y=16.3

z=73.7

Explanation:

Given :

`AC=x\,,\,AB= 7 \,\,in.\,,\,BC=24\,\,in.`

`\angle A=z\,,\,\angle C=y`

To find : x, y and z

Solution:

Pythagoras theorem:

In right angled triangle, square of hypotenuse is equal to sum of squares of the remaining two sides .

Here,
`\Delta ABC` is right angled at B

On applying pythagoras theorem, we get

`AC^2=AB^2+BC^2\\x^2=24^2+7^2\\x^2=576+49\\x^2=625\\x=25`

Also, we know that
`\tan \theta` = perpendicular/ Base

`\tan A=\tan z=(BC)/(AB)=(24)/(7)\\\\\Rightarrow z=\arctan \left ( (24)/(7) \right )=73.7`

`\tan C=\tan y=(AB)/(BC)=(7)/(24)\\\\\Rightarrow y=\arctan \left ( (7)/(24) \right )=16.3`