In the above triangle, if x = , y = 1, and z = 2, then which of the following is equal to tan(60°)? A. √(3) B. (√(2) )/(2) C. (√(3) )/(2) D. (√(3) )/(3)

Question

asked Sep 2, 2020 39.7k views

2 Answers

Superkhau · Answer 1 · 2020-09-03T02:18:23+0000

The answer is:

The correct option is:

A.
√(3)

Since we already know the hypothenuse and the opposite side of the triangle (y), we can calculate the value of "x" using the Pythagorean Theorem.

We have that:

Hypothenuse^(2)=Adjacent^(2)+Opposite^(2)

We know that:

$Hypothenuse=z=2\\Adjacent=x=1$

So, substituting and calculating we have:

2^(2)=1^(2)+Opposite^(2)

4-1=Opposite^(2)

$Opposite^(2)=3\\Opposite=√(3)$

Then,using the following trigonometric relation:

$Tan(\alpha)=(Opposite)/(Adjacent)\\\\Tan(60\°)=Tan((Opposite)/(Adjacent))=Tan((√(3) )/(1))^=\sqrt{3$

We have that the correct option is:

A.
√(3)

Have a nice day!

Axbeit · Answer 2 · 2020-09-07T20:01:59+0000

Answer: Option A

$tan(60\°) = √(3)$

Explanation:

We know the sides and z. So since it is a straight triangle we use the Pythagorean theorem to pull the length of the x side.

$z ^ 2 = x ^ 2 + y ^ 2\\\\x^2 = z^2 - y^2\\\\x=√(z^2 - y^2)\\\\x=√(2^2 - 1^2)\\\\x=√(4 - 1)\\\\x=√(3)$

By definition, the tangent of an angle is:

$tan(\theta) = (opposite)/(adjacent)$

In this case:

$adjacent = y=1\\\\opposite=x =√(3)\\\\\theta=60\°$

Then:

$tan(60\°) = (√(3))/(1)$

$tan(60\°) = √(3)$