Trigonometry Mixed Review: Part 1 (1)

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Question 1 of 9

1. Question
Which of the following are labelled correctly?

There can be more than one answer
- 1.
- 2.
- 3.
- 4.
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Check each triangle and identify if the labels are correct

The side opposite of the right angle is labelled as hyp

The side opposite of $theta$ is labelled as opp

The side adjacent to $theta$ is labelled as adj

The triangle is labelled correctly

The side opposite of the right angle is labelled as hyp

The side opposite of $theta$ is labelled as opp

The side adjacent to $theta$ is labelled as adj

The triangle is labelled correctly

The side opposite of the right angle is labelled as hyp

The side opposite of $theta$ is labelled as opp

The side adjacent to $theta$ is labelled as adj

The triangle is labelled correctly

The side opposite of the right angle is labelled as “opp”, but it should be hyp

The side opposite of $theta$ is labelled as “hyp”, but it should be opp

The side adjacent to $theta$ is labelled as adj

The triangle is labelled incorrectly

Question 2 of 9

Solve for:

$(i) \text(sin)theta$

$(ii) \text(cos)(90-theta)$

Enter fractions as: x/y

$\text(sin)theta =$ (3/5)
$\text(cos)(90 - theta) =$ (3/5)

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Sin Ratio

$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$

Cos Ratio

$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$

Tan Ratio

$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$

$\text(Solving for) (i) sin theta$

First we need to identify which trig ratio to use.

One of the known lengths $(3)$ is $\text(opposite)$ to

$theta$ and the other length $(5)$ is the $\text(hypotenuse)$

Hence, we can use the

$sin \text(ratio)$ to solve for

$sintheta$

$sin theta$	$=$	$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$	$sin \text(ratio)$

$cos theta$	$=$	$\frac{\color{#004ec4}{3}}{\color{#e85e00}{5}}$	Plug in the values

$\text(Solving for) (ii) cos (90-theta)$

First we need to understand which angle is

$(90-theta)$ .
Notice that the two known angles of the triangle is the right angle

$(90°)$ and

$theta$ .
Hence, the other angle left is

$(90-theta)$ .

Now, one of the known lengths $(3)$ is $\text(adjacent)$ to

$(90-theta)$ and the other length $(5)$ is the $\text(hypotenuse)$

Hence, we can use the

$cos \text(ratio)$ to solve for

$cos(90-theta)$

$cos (90-theta)$	$=$	$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$	$cos \text(ratio)$

$cos (90-theta)$	$=$	$\frac{\color{#00880a}{3}}{\color{#e85e00}{5}}$	Plug in the values

$sintheta=3/5$

$cos (90-theta)=3/5$

Question 3 of 9

3. Question
Solve for $x$ if:

$theta=30$
- $x=$ (60) $°$
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The sum of the interior angles of a triangle is $180$ degrees.

Identify the known values

$theta=30°$

$\text(right angle)=90°$

To solve for $x$ , we need to subtract the total value of the known angles from $180$ degrees

$x$ $=$ $180°-($ $theta$ $+$ $\text(right angle)$ $)$

$=$ $180°-($ $30°$ $+$ $90°$ $)$ Plug in the values

$=$ $180°-120°$ Evaluate

$x$ $=$ $60°$

$x=60°$

Question 4 of 9

Solve for

$theta$

Round your answer to the nearest degree

$theta=$ (37) $°$

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