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
