Question

If 3^x-2 = 9 and the side of the sail, which is the hypotenuse to the right triangle, is 7 meters long, what is the value of tan⁡50∘77tan50∘​?

a) 7tan⁡50∘
b) 7sin⁡50∘
c) tan⁡50∘/7
d) sin⁡50∘/7​

Answer 1

The correct answer to the student's question is option (a) 7tan 50°, as tan of an angle in a right triangle is a ratio of the opposite side to the adjacent side, and the student is asking to multiply this ratio by the hypotenuse length (7 meters).

Step-by-step explanation:

To solve the question, we must understand that the given inequality, 3^x-2 = 9, is not directly tied to the question about tan 50°. Instead, the central focus is on the right triangle and its properties. The Pythagorean theorem, which states a² + b² = c², helps us relate the lengths of the legs of the triangle to its hypotenuse.

Specific to this student's question regarding what tan 50° multiplied by the hypotenuse length (7 meters) would be, we can rule out options that mention sine, as the student is specifically asking about the tangent. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side (tan θ = opposite/adjacent).

Thus, the correct representation for the tangent would simply multiply the tangent value by the length of the hypotenuse, which aligns with option (a) 7tan 50°.