Question

question 36 of 50
the value of x is:
triangle with right angle, one leg 8, angle 45°, hypotenuse x
options: 11.3, 16, 8

Explanation:

Step1: Identify Triangle Type

The triangle is right - angled with one angle \(45^{\circ}\), so it's a 45 - 45 - 90 triangle (isosceles right triangle), where legs are equal and hypotenuse \(= \text{leg}\times\sqrt{2}\). Here, one leg is 8, and the hypotenuse is \(x\)? Wait, no, wait. Wait, in the right - angled triangle, if one non - right angle is \(45^{\circ}\), the other non - right angle is also \(45^{\circ}\) (since triangle angles sum to \(180^{\circ}\), \(180 - 90 - 45=45^{\circ}\)). So the two legs are equal? Wait, no, the side labeled 8 is a leg, and the side labeled \(x\) is the hypotenuse? Wait, no, wait, maybe I misread. Wait, in a 45 - 45 - 90 triangle, legs are equal, and hypotenuse \(= \text{leg}\times\sqrt{2}\). But if the leg is 8, then hypotenuse \(x = 8\sqrt{2}\approx8\times1.414 = 11.31\approx11.3\).

Step2: Calculate Hypotenuse

Using the formula for hypotenuse (\(c\)) in a 45 - 45 - 90 triangle, where \(a = b = 8\) (legs), \(c=a\sqrt{2}\). So \(x = 8\sqrt{2}\approx11.3\).

Answer:

11.3