Question

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To indirectly measure the distance across a river, Isaiah stands on one side of the
river and uses sight-lines to a landmark on the opposite bank. Isaiah draws the
diagram below to show the lengths and angles that he measured. Find PR, the
distance across the river. Round your answer to the nearest foot.
R
150

Answer 1

The question is an illustration of similar triangles.

The distance across the river is 500ft

From the question (see attachment), we have:

$\mathbf{RO = 170}$

$\mathbf{RE = 250}$

$\mathbf{OC = 335}$

Because, triangles PRE and POC are similar, we can make use of the following equivalent ratios

$\mathbf{PR:RE = PO:OC}$

Where:

$\mathbf{ PO = PR + RO}$

Express $\mathbf{PR:RE = PO:OC}$ as a fraction

$\mathbf{\frac{PR}{RE} = \frac{PO}{OC}}$

Substitute$\mathbf{ PO = PR + RO}$

$\mathbf{\frac{PR}{RE} = \frac{PR + RO}{OC}}$

Substitute known values

$\mathbf{\frac{PR}{250} = \frac{PR + 170}{335}}$

Cross multiply

$\mathbf{335 \times PR = 250 \times (PR + 170)}$

Open brackets

$\mathbf{335 \times PR = 250 \times PR + 250 \times 170}$

Collect like terms

$\mathbf{335 \times PR - 250 \times PR = 250 \times 170}$

Factor out PR

$\mathbf{(335 - 250) \times PR = 250 \times 170}$

Make PR the subject

$\mathbf{PR = \frac{250 \times 170}{(335 - 250)}}$

$\mathbf{PR = \frac{42500}{85}}$

$\mathbf{PR = 500}$

Hence, the distance across the river is 500ft

Read more about similar triangles at:

https://brainly.com/question/20502441

Answer 2

Answer: The distance across the River is 258 ft.