Triangles

9000035006

Level:

A ladder of the length

15 m

leans against a wall. The angle between the ladder and the horizontal direction is

70^{\circ}

. Find the height of the top of the ladder and round your answer to the nearest meters.

14 m

13 m

16 m

15 m

9000035007

Level:

A roof gable has the shape of an isosceles triangle with the base of

14 m

. The angle between the roof and the horizontal direction is

31^{\circ}

. Find the height of the gable. Round your result to one decimal place.

4.2 m

5.9 m

3.6 m

11.2 m

9000035008

Level:

Sun shines to the road at the angle

53^{\circ} 22^{'}

. An electric column near the road casts the shadow of the length

4.5 m

. Find the height of the column and round your answer to the nearest meters.

6 m

3 m

4 m

5 m

9000035009

Level:

Two forces act on the body at one point. The force

F_{1} = 760 N

acts horizontally from left to the right and the force

F_{2} = 28.8 N

acts vertically from the top to the bottom. Find the angle between the horizontal direction and the direction of the resulting force and round your answer to the nearest degrees and minutes.

2^{\circ} 10^{'}

3^{\circ} 10^{'}

2^{\circ} 20^{'}

3^{\circ} 20^{'}

9000045701

Level:

The right angled triangle

A B C

is given (see the picture). Choose the correct statement.

\cos β = \frac{a}{c}

\cos β = \frac{b}{c}

tg α = \frac{b}{a}

\sin α = \frac{c}{a}

9000045702

Level:

Given a right triangle

A B C

(see the picture). Find the valid relation between the angle

α

and the sides of the triangle.

tg α = \frac{a}{c}

\sin α = \frac{a}{c}

\cos α = \frac{b}{a}

cotg α = \frac{b}{a}

9000045703

Level:

Given a right triangle

A B C

with the right angle at

C

and an altitude

v

(see the picture). Find the valid relation between the angle

α

and the lengths in the triangle.

\sin α = \frac{v}{b}

\sin α = \frac{v}{c}

\sin α = \frac{a}{v}

\sin α = \frac{c}{a}

9000045704

Level:

Given a right triangle

A B C

with the right angle at

C

and an altitude

v

(see the picture). Find the valid relation between the angle

β

and the lengths in the triangle.

\sin β = \frac{v}{a}

tg β = \frac{a}{v}

\cos β = \frac{v}{a}

tg β = \frac{v}{a}

9000046403

Level:

Consider an isosceles triangle, i.e. the triangle with two sides of equal length. The length of the third side is

4 cm

. One of the interior angles is

120^{\circ}

. Find the area of this triangle.

\frac{4 \sqrt{3}}{3} {cm}^{2}

4 \sqrt{3} {cm}^{2}

\frac{8 \sqrt{3}}{3} {cm}^{2}

1003021902

Level:

What is the width of a computer screen if the ratio of its width and height is

16 : 9

and the computer has

23

-inch monitor? Round the result to two decimal places. (

1

inch=

2.54 cm

)

50.92 cm

20.05 cm

11.28 cm

28.65 cm

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1003021902

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