If you learned about the 45-45-90 triangle (which is isosceles), then the faster way is to know that the hypotenuse (side opposite of right angle) is √2 times either one of the sides. 3√2 = (√2)x x = 3
But if you didn't learn the 45-45-90 triangle yet, that's ok. Recall the trigonometric ratios for right triangles: sine (sin), cosine (cos), tangent (tan).
If your angle is x, then sin(x) = opposite side / hypotenuse cos(x) = adjacent side / hypotenuse tan(x) = opposite side / adjacent side
Remember the hypotenuse is the side opposite and across from the right angle (3√2 in this case). An acronym to remember this is SohCahToa.
In this problem, the angle given is 45°, and you need to find the length of the adjacent side x. The hypotenuse is also given as 3√2.
Because we have the adjacent side and the hypotenuse, we use cosine to relate those two sides cos(45°) = x / (3√2) x = (3√2)cos45° If you plug this into your calculator (in degree mode), then x = 3
The formula for the area of a triangle is a=bh/2, where a is area, b, is the base, and h is the height. If we substitute the values in the question in the equation, we get:
