Math  /  Trigonometry

QuestionA ladder seven meters in length leans against a building. If the angle of elevation of the ladder with the ground 7070^{\circ}, how far up the wall does the ladder reach? 6.57 meters 5.18 meters 4.98 meters 2.39 meters

Studdy Solution
Solve for the height the ladder reaches on the wall:
Height=7×sin(70) \text{Height} = 7 \times \sin(70^\circ)
Calculate sin(70)\sin(70^\circ):
sin(70)0.9397 \sin(70^\circ) \approx 0.9397
Substitute this value into the equation:
Height=7×0.9397 \text{Height} = 7 \times 0.9397 Height6.5779 \text{Height} \approx 6.5779
Round to two decimal places:
Height6.58 meters \text{Height} \approx 6.58 \text{ meters}
The ladder reaches approximately 6.58 6.58 meters up the wall, which is closest to 6.57 6.57 meters.
The correct answer is:
6.57 meters \boxed{6.57 \text{ meters}}

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