Question
Consider the following triangle (not drawn to scale). A diagram showing a right-angled triangle. Starting from the right angle the sides are labelled nothing, square root of 2 and 1. Going round the triangle in the same order, starting from the right angle the second angle is labelled theta. Select the option that is the value of the angle marked θ. (Hint: you should not need to calculate anything as the given triangle is one of the standard triangles used to calculate useful known values of sine, cosine and tangent.)
Answer
4.7
(1 Votes)
Kyla
Professional · Tutor for 6 years
Answer
## AnswerThe triangle you're referring to is a special right triangle, specifically a 45-45-90 triangle. This is because the sides are in the ratio 1:1:√2, which is characteristic of a 45-45-90 triangle.In a 45-45-90 triangle, the two angles other than the right angle (90 degrees) are both 45 degrees. This is because the sum of the angles in a triangle is always 180 degrees, so if one angle is 90 degrees, the other two must add up to 90 degrees. Since the two angles are equal (as indicated by the equal sides), they must each be 45 degrees.Therefore, the angle marked θ in your triangle is **45 degrees**.Here's a summary of the properties of a 45-45-90 triangle:| Angle | Side Opposite | Side Adjacent | Hypotenuse ||-------|---------------|---------------|------------|| 45° | 1 | 1 | √2 || 45° | 1 | 1 | √2 || 90° | √2 | 1 | 1 |Remember, the sides are in the ratio 1:1:√2, and the angles are 45°, 45°, and 90°.