gilcarrillo146
29.07.2019 •
Mathematics
Dante is standing at horizontal ground level with the base of the empire state building in new york city. the angle formed by the ground and the line segment from his position to the top of the building is 48.4°. the height of the empire state building is 1,472 feet. find his distance from the empire state building to the nearest foot.
a. 7.65 ft
b. 1, 968 ft
c. 1,307 ft
d. 2, 217 ft
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Ответ:
C. 1307 ft
Step-by-step explanation:
Given:
Angle = 48.4 degrees
Height, opposite side= 1472 feet
his distance from the Empire State Building, base=x
Now as per the trigonometric ratios:
Tan∅= Opposite/base
tan(48.4)= 1472/x
x=1472/(1.13)
x=1302.65
his distance from the Empire State Building is 1302.65 feet!
Ответ:
Please look at the steps below.
Step-by-step explanation:
1) m∠BAC=m∠CAD, m∠ACB=m∠ADC=90 degrees , then m<ABC=m∠ACD.
Therefore, triangles ADC and ACB are similary by AAA theorem.
2)AC /AB = AD/AC
3) Substituting the lengths, we get b/c = e/b
4) Cross multiplying the ratio, we get b^2 = ce
5) m∠ABC=m∠CBD, m∠ACB=m∠CDB=9, then m∠BAC=m∠BCD and the triangles BDC and BCA are similar by AAA theorem.
6) The ratio of the corresponding sides of similar triangles is in proportion.
BC/BD = AB/BC
7) Substituting the lengths, we get a/d = c/a
8) a^2 = cd
9) Add the results in 4) and 8), we get b^2 + a^2 = ce + cd
10) b^2 + a^2= c(e + d)
11) e + d =c, when we plug in step 10, we get a^2 + b^2 = c.c
a^2 + b^2 = c^2.
Hope this will helpful.
Thank you.