Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Trigonometry Problem: Finding an Angle in a Right Triangle
#### Problem Statement
**Incorrect**
What is \( m \angle G \) to the nearest tenth?
#### Diagram Description
The image depicts a right triangle \( \triangle GEF \):
- The right angle is at vertex \( F \).
- The side \( GF \) (the base) measures \( 45.8 \) units.
- The side \( FE \) (the height) measures \( 28.2 \) units.
- The side \( GE \) is the hypotenuse.
#### Educational Objective
Determine the measure of angle \( G \) in \(\triangle GEF \) to the nearest tenth of a degree using trigonometric principles.
#### Solution Steps
1. **Identify the sides relative to \(\angle G \):**
- Opposite to \(\angle G\): \( FE = 28.2 \) units
- Adjacent to \(\angle G\): \( GF = 45.8 \) units
2. **Use the tangent function:**
\[
\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}
\]
\[
\tan(G) = \frac{FE}{GF} = \frac{28.2}{45.8}
\]
3. **Calculate the angle:**
\[
\theta = \tan^{-1}\left(\frac{28.2}{45.8}\right)
\]
4. **Use a calculator to find the inverse tangent:**
\[
\theta \approx \tan^{-1}(0.615)
\]
\[
\theta \approx 31.8^\circ
\]
Thus, the measure of \( m \angle G \) to the nearest tenth is approximately \( 31.8^\circ \).
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This is an essential exercise in trigonometry where students learn how to apply the tangent function and inverse trigonometric functions to find unknown angles in right triangles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07a88fff-47cb-4f0b-a013-c1ee90395962%2F102ff5e1-bdcd-4a45-992a-22c21519972a%2Fyeocw8_processed.jpeg&w=3840&q=75)
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