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

Answers:
x = 25 in
y = 16.3°
z = 73.7°

Explanation:
Part (a): getting the value of x:
Since the given triangle is a right-angled triangle, we can get the value of x which is the hypotenuse of the triangle using the Pythagorean theorem as follows:
(hypotenuse)² = (side1)² + (side2)²
x² = (24)² + (7)²
x² = 625
x = √625
either x = 25 in > accepted
or x = -25 in > rejected as side length cannot be negative.
Based on the above:
x = 25 in

Part (b): getting the value of y:
Since the given triangle is a right-angled triangle, therefore, special trigonometric functions can be applied.
These functions are as follows:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
In the given, we have:
θ = y
opposite side = 7 in
adjacent side = 24 in
Apply in the tan formula:
tan y = 7/24
y = 16.3° to the nearest tenth

Part (c): getting the value of z:
This can be solved in two ways:
Solution 1: Using angles
Sum on internal angles in a triangle is 180
90 + 16.3 + z = 180
z = 73.7°
Solution 2: Using special trig functions:
We have θ = z
opposite side = 24 in
adjacent side = 7 in
tan z = 24/7
z = 73.7° to the nearest tenth

Hope this helps :)

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