Question

Fill in the blank. In the triangle below, z° =

Answer: _____°. _______
The triangle here --> http://imgur.com/mTAiNJo


Fill in the blank. In the triangle below, x = ______. Round your answer to two decimal places.
The triangle here --> http://imgur.com/4s0aoP7


Fill in the blank. In the triangle below, y = ______. Round your answer to two decimal places.
The triangle here --> http://imgur.com/jRjOMAr

Answer 1

Answer on Question #58327 – Math – Trigonometry

Question

1. Fill in the blank. In the triangle below, $z{}^{\circ} =$

Solution

The first angle equals $42{}^{\circ}$, the next angle is $90{}^{\circ}$, and the third angle equals $z{}^{\circ}$.

The sum of interior angles of any triangle is equal to $180{}^{\circ}$:

$$42{}^{\circ} + 90{}^{\circ} + z{}^{\circ} = 180{}^{\circ},$$

hence

$$z{}^{\circ} = 180{}^{\circ} - 42{}^{\circ} - 90{}^{\circ} = 180{}^{\circ} - 132{}^{\circ} = 48{}^{\circ}.$$

ANSWER: $z{}^{\circ} = 48{}^{\circ}$

Question

2. Fill in the blank. In the triangle below, $x =$ _______. Round your answer to two decimal places.

Solution

First of all, let's find $z{}^{\circ}$, and then we can use a value of $\tan(z{}^{\circ})$ to obtain $x$.

$$\begin{array}{l} z{}^{\circ} = 180{}^{\circ} - 52{}^{\circ} - 90{}^{\circ} = 38{}^{\circ}, \\ \tan(38{}^{\circ}) = \frac{35}{x}, \end{array}$$

hence

$$x = \frac{35}{\tan(38{}^{\circ})} = \frac{35}{0.7812856265} \approx 44.80.$$

ANSWER: $x \approx 44.80$

Question

3. Fill in the blank. In the triangle below, $y =$ ______. Round your answer to two decimal places.

Solution

In part 2 we have already found $z{}^{\circ} = 38{}^{\circ}$ and $x = 44.80$.

Now, in order to calculate the value of $y$, we shall use the Pythagorean theorem ($a^2 + b^2 = c^2$):

$$y^2 = x^2 + 35^2 = 44.80^2 + 35^2,$$

hence

$$y = \sqrt{44.80^2 + 35^2}.$$

ANSWER: $y \approx 56.85$.

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