I am lost with this trig. question, what please is the answer, steps would help me.?

Question

Use the given triangles to evaluate the expression. Rationalize all denominators.

I have two right triangles of a different size. The legs of the smaller triangle are both 1, and the hypotenuse is sqrt2, and the two acute angles inside the triangle are both 45 degrees.

The bigger right triangle has a small leg of 1, and the long leg of sqrt3, and a hypotenuse of two, the two angles inside of it are 60, and 30 degrees


tan 45° - sin 45°

I know asked for help and all, but shouldn't the correct answer be 2-sqrt2/2?!

Answer 1

You don't need the second triangle for this.
The tangent of a non-right angle in a right triangle is the ratio of the opposite to adjacent leg. In the case of the 45 degree angle, they are equal, so the tangent=1. The sine of a non-right angle in a right triangle is the ratio of the opposite leg to the hypotentuse. In this case, the result is 1/sqrt(2).
We can multiply the num. and denom. of this by sqrt(2) to get sqrt(2)/2. So the expression is
1- sqrt(2)/2.

Answer 2

Greetings

Using the 1, 1 , sqrt(2) triangle find the values for tan 45 = 1 (opposite side/ adjacent side) and sin 45 = 1 / sqrt(2) = sqrt(2)/2 (opposite side/hypotenuse)

Then tan 45° - sin 45° = 1 - sqrt(2)/2

Regards