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7 votes
7 votes
Find the lengths of segment RS and segment QS

User Thastark
by
2.9k points

1 Answer

13 votes
13 votes

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

angle = 30°

opposite = QR = 7

RS = ?

QS = ?

Step 02:

tan α = opposite / adjacent

RS = adjacent

tan 30 = 7 / RS

RS * tan 30 = 7

RS = 7 / tan 30 = 7 / (√3 / 3) = 7 * 3 / √3 = 21 / √3 = 7 √3

QS = hypotenuse

sin α = opposite / hypotenuse

sin 30 = 7 / QS

QS * sin 30 = 7

QS = 7 / sin 30 = 7 / (1 /2) = 14

The answer is:

RS = 7 √3

QS = 14

User Robert Iver
by
2.9k points