To find the height of the tree (labeled
x), we can use trigonometry. Here is the step-by-step solution:
1. Identify the parts of the triangle:
* The triangle is a right-angled triangle because the tree stands straight up from the ground (indicated by the square symbol at corner C).
* The angle at A is
35°.
* The side next to the angle (the distance along the ground) is
47. This is called the
Adjacent side.
* The side opposite the angle (the height of the tree) is
x. This is called the
Opposite side.
2. Choose the correct formula:
We need a formula that connects the Opposite side, the Adjacent side, and the angle. The tangent function (tan) does exactly this:
$$ \tan(\text{angle}) = \frac{\text{Opposite}}{\text{Adjacent}} $$
3. Set up the equation:
Substitute the known values into the formula:
$$ \tan(35^\circ) = \frac{x}{47} $$
4. Solve for x:
To get
x by itself, multiply both sides by 47:
$$ x = 47 \times \tan(35^\circ) $$
5. Calculate the value:
First, find the value of $\tan(35^\circ)$ using a calculator:
$$ \tan(35^\circ) \approx 0.7002 $$
Now, multiply by 47:
$$ x \approx 47 \times 0.7002 $$
$$ x \approx 32.91 $$
Rounding to one decimal place, the height is
32.9.
Final Answer:
32.9
Parent Tip: Review the logic above to help your child master the concept of trig word problems worksheet answer key.
