2000003201
Level:
A
There is a triangle ABC in the picture. Choose the correct statement.
The triangle is isosceles.
The triangle is equilateral.
The triangle is right-angled.
The triangle is obtuse.
Triangles
Triangle trigonometry
Submitted by ladislav.foltyn on Sun, 03/17/2019 - 13:39Question:
An equilateral triangle and a square are in the diagram. Refer to the diagram and in the table mark the right values of trigonometric functions for the given angles.
Finding the Third Angle in a Triangle
Submitted by ladislav.foltyn on Sat, 02/23/2019 - 14:08Question:
Find the third angle of a triangle if the other two angles are known.
Adjacent, Vertical and Supplementary Angles
Submitted by ladislav.foltyn on Mon, 12/10/2018 - 12:33Question:
Follow the diagram and assign the correct degree measure to each angle in the table.
Right triangle trigonometry
Question:
The diagram shows a right-angled triangle with the right angle at the vertex $C$. Mark the appropriate fraction that defines the goniometric function in the triangle for each of the given goniometric functions.
1103077105
Level:
C
In a triangle \( ABC \), \( a=7\,\mathrm{cm} \), \( b=8\,\mathrm{cm} \), \( c=11\,\mathrm{cm} \). What is the radius of a circle circumscribed about this triangle? Round the result to two decimal places.
\( 5.51\,\mathrm{cm} \)
\( 6.11\,\mathrm{cm} \)
\( 4.92\,\mathrm{cm} \)
\( 6.52\,\mathrm{cm} \)
1103077104
Level:
C
Three equal circles, each of radius \( 6\,\mathrm{cm} \), touch each other as shown in the figure. Find the area of the region bounded by the circles. Round the result to one decimal place.
\( 5.8\,\mathrm{cm}^2 \)
\( 62.3\,\mathrm{cm}^2 \)
\( 6.2\,\mathrm{cm}^2 \)
\( 8.4\,\mathrm{cm}^2 \)
1103077102
Level:
A
Derive the formula for calculating the perimeter of an equilateral triangle circumscribed about a circle of radius \( r \).
\( 6\sqrt3 r \)
\( 2\sqrt3 r \)
\( \frac{2r}{\sqrt3} \)
\( \frac{6r}{\sqrt3} \)
1103077101
Level:
A
Derive the formula for calculating the perimeter of an equilateral triangle inscribed in a circle of radius \( r \).
\( 3\sqrt3 r \)
\( \sqrt3 r \)
\( 3 r \)
\( \frac{3\sqrt3 r}2 \)
1103021907
Level:
C
A plane is flying at a speed of \( 900\,\mathrm{km}\cdot\mathrm{h}^{-1} \) and according to the compass the axis of the airplane is still heading westbound. What angle will the flight path of the airplane make with the east-west direction if the south wind starts to blow at a speed of \( 10\,\mathrm{m}\cdot\mathrm{s}^{-1} \)? Round the result to two decimal places.
\( 2.29^{\circ} \)
\( 0.64^{\circ} \)
\( 0.01^{\circ} \)
\( 87.71^{\circ} \)