If 3 tan A = 4 and A is an acute angle, then find the value of 4 sin A + 3 cos A.

Question

Accepted Answer

Given: 3 tan A = 4
=> tan A = 4/3

Since A is acute, we can consider a right triangle where opposite side = 4, adjacent side = 3.

Hypotenuse = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5

sin A = opposite/hypotenuse = 4/5
cos A = adjacent/hypotenuse = 3/5

Calculate 4 sin A + 3 cos A:
= 4 * (4/5) + 3 * (3/5)
= (16/5) + (9/5)
= 25/5
= 5

However, the options given are 1, 4, 5, 3. The calculation shows 5.

But let's re-check the problem statement and options carefully.

Wait, the options are:
1. 1
2. 4
3. 5
4. 3

Our calculation shows 5, which corresponds to option 3.

Therefore, the correct answer is 5.

Answer

Answer

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