A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along
the diagonal of the smaller rectangular section. What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines? 21.2 m 27.5 m 32.5 m 38.2 m
2 answers:
the picture in the attached figure
Applying the Pythagorean Theorem
Find the lengths of the two sidewalks
Step 1
square section
D=√{15²+15²}
D=√450 m
D=21.21 m
Step 2
rectangular section
D=√{15²+8²}
D=√289 m
D=17 m
Step 3
the sum of the lengths of the diagonals of the two sections is
17m + 21.21 m = 38.21 m
the answer is
38.2 m
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Answer:
54.8 feet
Step-by-step explanation:
We assume that the distance of interest is the direct line distance from the observation point to the bottom of the monument, segment PH in the diagram below.
This can be found using the Law of Sines.
∠PMH is the complement of the angle of elevation to the top of the monument, so is 40°.
∠MPH is the difference in the angles of elevation, so is 28°.
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The Law of Sines tells us the ratio of side lengths is the same as the ratio of the sines of the opposite angles, so ...
PH/MH = sin(∠PMH)/sin(∠MPH) = sin(40°)/sin(28°)
Multiplying by MH, we can find the length of PH:
PH = (40 ft)(sin(40°)/sin(28°)) ≈ 54.7669 ft
PH ≈ 54.8 ft . . . . the distance Pete must climb to reach the monument.
