Step: 1

Length of the pillar, a = 227 ft.

Step: 2

Length of the shadow, b = 363 ft.

Step: 3

Step: 4

Step: 5

In right triangle ABC, tan C = 2 2 7 3 6 3

[Use tan C = A B B C = a b .]

Step: 6

tan C ≈ 0.625344

[Simplify.]

Step: 7

[Use calculator to find the measure of ∠ C.]

Step: 8

So, angle of elevation of the sun is 32°

Correct Answer is : 32°

Step: 1

Let AB be the height of the tower and C be the position of boy in the figure.

AB = 282 m and AC = 168 m.

AB = 282 m and AC = 168 m.

Step: 2

Step: 3

[AC ¯ and BX ¯ are parallel, the angles of elevation and depression are equal in measure.]

Step: 4

In right triangle CAB, tan C = 2 8 2 1 6 8 ≈ 1.6969

[Use tan C = A B A C .]

Step: 5

[Use calculator to find the measure of ∠ C.]

Step: 6

Angle of depression of the boy from the top of the tower is 59° 13′.

Correct Answer is : 53° 26′

Step: 1

Let the height of the flagpole, BC = h and the height of the building, AB = x

Step: 2

D is the point of observation.

Step: 3

tan 57°20′ = x 2 3 0

[tan ∠ BDA = A B A D .]

Step: 4

Step: 5

tan 70°15′ = x + h 2 3 0

[tan ∠ CDA = A C A D .]

Step: 6

Step: 7

Step: 8

359 + h = 641

Step: 9

Step: 10

So, the height of flagpole is 282 ft.

Correct Answer is : 331 ft

Step: 1

Height of the pole, PQ = 120 m and R & S be the position of boys on either side of the pole.

Step: 2

tan 30°20′ = 1 2 0 Q R

[tan R = P Q Q R .]

Step: 3

QR = 1 2 0 tan 3 0 o 2 0 '

Step: 4

QR ≈ 205 m

Step: 5

tan 4 5 o 3 0 ' = 1 2 0 Q S

[tan S = P Q Q S .]

Step: 6

QS = 1 2 0 tan 4 5 o 3 0 ' ≈ 118 m

Step: 7

RS = QR + QS = 205 + 118 = 323 m

Step: 8

So, the distance between the boys is 323 m.

Correct Answer is : 350 m

Step: 1

Let x represent the height of the tower.

Step: 2

In right triangle PAB,

Step: 3

tan 60° = x 2 5 .

Step: 4

Step: 5

Step: 6

The height of the tower is 43 ft.

Correct Answer is : 43 ft

Step: 1

Draw the figure from the given data.

Step: 2

Step: 3

Let x be the distance of point P from the foot of the tower.

Step: 4

Height of the tower A B = y = 130 m

[Given.]

Step: 5

In right triangle P A B , tan 60° = 1 3 0 x .

Step: 6

Step: 7

[Substitute the value of tan 60°.]

Step: 8

So, the distance of the point P from the foot of the tower = 1 3 0 3 m.

Correct Answer is : 1 1 9 3 m

Step: 1

The measure of the angle of elevation from point A is 35°.

Step: 2

In right triangle APQ, tan 35° = h 2 5

[l = 22 ft.]

Step: 3

[Substitute the value of tan 35°.]

[Use calculator.]

[Use calculator.]

Step: 4

[Simplify.]

Step: 5

So, the height of the tree is 18 ft.

Correct Answer is : 9 ft

Step: 1

Draw a figure for the given data.

Step: 2

Step: 3

In right triangle P Q S , tan 40° = y 2 4

Step: 4

Step: 5

In right triangle PQR, tan 55° = x + y 2 4

Step: 6

Step: 7

[Substitute the value of tan 55° .]

Step: 8

[Substitute the value of y .]

Step: 9

Step: 10

Height of the flagstaff is 14 ft.

Correct Answer is : 12 ft

Step: 1

Draw the figure from the given data.

Step: 2

Let AB represent the first building and CE represent the opposite building.

Step: 3

[The opposite sides of a rectangle.]

Step: 4

In right triangle ABC , tan 25° = A B B C

Step: 5

[Substitute the value of tan 25° and simplify.]

Step: 6

Step: 7

[Opposite sides of a rectangle.]

Step: 8

In right triangle ADE , tan 40° = D E A D

Step: 9

[From step 7.]

Step: 10

[Substitute the value of tan 40° and simplify.]

Step: 11

Therefore, the height of the opposite building CE = CD + DE

Step: 12

Step: 13

Step: 14

Therefore, the height of the opposite building is 197 meters.

Correct Answer is : 260 meters

Step: 1

Draw the figure for the given data.

Step: 2

Height of the first tower, AB = 130 ft

Step: 3

Height of the second tower, CD = 86 ft

Step: 4

Let the distance between the two towers, BC = ED = x ft.

Step: 5

Let the difference between the heights of the two towers, AE = h ft.

Step: 6

In right triangle AED , tan 20° = A E E D = h x

⇒ h = 0.36x

[Substitute the value of tan 20° and simplify.]

Step: 7

From the figure, AE = AB - BE

⇒ AE = 130 - 86 = 44 ft.

[From the figure AE = h .]

Step: 8

44 = 0.36x

[From step 6 and step 7.]

Step: 9

Step: 10

So, the distance between the two towers is 122 ft.

Correct Answer is : 109 ft

Step: 1

Let b be the height of the tower.

Step: 2

tan 52° = b 2 2

Step: 3

Step: 4

Step: 5

So, the height of the tower is 28 ft.

Correct Answer is : 28 ft

Step: 1

Let AD = 140 m, be the height of the building and B & C be the position of boys on either side of the building with ∠ B = 30°18′ and ∠ C = 40°20′ .

Step: 2

tan 30°18′ = 1 4 0 D B

[tan B = A D D B .]

Step: 3

DB = 1 4 0 tan 3 0 o 1 8 '

Step: 4

DB = 240 m

Step: 5

tan 4 0 o 2 0 ' = 1 4 0 D C

[tan C = A D D C .]

Step: 6

DC = 1 4 0 tan 4 0 o 2 0 ' = 165 m

Step: 7

BC = DB + DC = 240 + 165 = 405 m

Step: 8

So, the distance between the boys is 405 m.

Correct Answer is : 405 m

Step: 1

Let MN = 180 m be the length of the tree.

Step: 2

Let MO = 120 m be the distance of the girl from the base of the tree.

Step: 3

[MO ¯ and NP ¯ are parallel, the angles of elevation and depression are equal in measure.]

Step: 4

tan O = 1 8 0 1 2 0

[tan O = M N M O .]

Step: 5

Correct Answer is : 56°18′

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