7. A
a. Draw a diagram to represent the situation.
b. Use your knowledge of trigonometric ratios to calculate how high up the wall the ladder will reach.
c. How far will the foot of the ladder be from the base of the building?
ladder, of length 5 metres, is placed against a wall at an angle of 65° to the horizontal.
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What situation? Cannot copy and paste or draw on these posts.
To answer this question, we can use trigonometric ratios to calculate the height and distance of the ladder on the wall. Let's go step by step:
a. To draw the diagram representing the situation, start by drawing a straight vertical line to represent the wall. Then, draw a line starting from the bottom of the wall at an angle of 65 degrees to the horizontal line. This line represents the ladder leaning against the wall. Label the length of the ladder as 5 meters.
b. To find out how high up the wall the ladder will reach, we can use the sine ratio. The sine of an angle is equal to the ratio of the opposite side to the hypotenuse in a right triangle. In this case, the opposite side is the height of the ladder on the wall, and the hypotenuse is the length of the ladder.
Using the sine ratio, we can write the equation: sin(angle) = opposite/hypotenuse
sin(65°) = height of ladder on the wall / 5m
Now, we can solve this equation to find the height of the ladder on the wall:
height of ladder on the wall = sin(65°) * 5m
Evaluate sin(65°) using a calculator or trigonometric table, and then multiply it by 5 meters to get the answer.
c. To find how far the foot of the ladder will be from the base of the building, we can use the cosine ratio. The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse in a right triangle. In this case, the adjacent side is the distance of the foot of the ladder from the base of the building, and the hypotenuse is the length of the ladder.
Using the cosine ratio, we can write the equation: cos(angle) = adjacent/hypotenuse
cos(65°) = distance of the foot of the ladder from the base / 5m
Now, we can solve this equation to find the distance of the foot of the ladder from the base:
distance of the foot of the ladder from the base = cos(65°) * 5m
Evaluate cos(65°) using a calculator or trigonometric table, and then multiply it by 5 meters to get the answer.