Given that sin A = 1/sqrt 26 and tan B = 1, and that angles A and B are both in Quadrant 1, find the exact value of sin(A + B), in simplest radical form.​

Step-by-step explanation:

Let’s find some exact values using some well-known triangles. Then we’ll use these exact values to answer the above challenges.

sin 45°: You may recall that an isosceles right triangle with sides of 1 and with hypotenuse of square root of 2 will give you the sine of 45 degrees as half the square root of 2.

45-45 trianglesin 45

sin 30° and sin 60°: An equilateral triangle has all angles measuring 60 degrees and all three sides are equal. For convenience, we choose each side to be length 2. When you bisect an angle, you get 30 degrees and the side opposite is 1/2 of 2, which gives you 1. Using that right triangle, you get exact answers for sine of 30°, and sin 60° which are 1/2 and the square root of 3 over 2 respectively.

equilateral triangle

sin 30

sin 60

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