a ladder leans against the sufe of a house. the angle of elevation of the ladder is 70 degrees when the bottom of the ladder is
1 answer:
Answer:
≈ 35.1 ft
Step-by-step explanation:
The model is a right triangle with ladder being the hypotenuse and the angle between the ground and the ladder is 70°
Using the cosine ratio, with l being the length of the ladder.
cos70° = =
( multiply both sides by l )
l × cos70° = 12 ( divide both sides by cos70° )
l = ≈ 35.1 ( to the nearest tenth )
The ladder is approx 35.1 ft long
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<u>Given</u>:
The exterior angle P is 74°
The measure of ∠PRQ is 51°
We need to determine the measure of ∠PQR
<u>Measure of ∠QPR:</u>
From the figure, it is obvious that P is the intersection of the two lines.
The angle 74° and ∠QPR are vertically opposite angles.
Since, vertically opposite angles are always equal, then the measure of ∠QPR is 74°
Thus, the measure of ∠QPR is 74°
<u>Measure of ∠PQR:</u>
The measure of ∠PQR can be determined using the triangle sum property.
Thus, we have;
Substituting the values, we get;
Thus, the measure of ∠PQR is 55°
Hence, Option B is the correct answer.