A man who is 70 inches tall has a shadow that is 80 inches long. A nearby tree casts a shadow that is 164 inches long. The shadow of the man and the shadow of the tree form similar triangles. How tall is the tree in inches?(1 point)

Answer 1

To find the height of the tree, we can use the concept of similar triangles. The ratio of the man's height to his shadow's length will be the same as the ratio of the tree's height to its shadow's length.

Let \( h \) be the height of the tree. We have the following ratios based on the information given:

\[ \frac{\text{Height of man}}{\text{Shadow of man}} = \frac{\text{Height of tree}}{\text{Shadow of tree}} \]

Plugging in the values:

\[ \frac{70 \text{ inches}}{80 \text{ inches}} = \frac{h}{164 \text{ inches}} \]

Now, we cross-multiply to solve for \( h \):

\[ 70 \times 164 = 80 \times h \]

Calculating the left side:

\[ 70 \times 164 = 11480 \]

So we have:

\[ 11480 = 80h \]

Now, divide both sides by 80 to find \( h \):

\[ h = \frac{11480}{80} \]

Calculating \( h \):

\[ h = 143.5 \]

Therefore, the height of the tree is \( \boxed{143.5} \) inches.