The value of the \(n\)th term of a sequence is given by the expression \(b^{2n}-28\). If the third term of the sequence is \(701\), which of the following is the value of \(b\)?
The value of the \(n\)th term of a sequence is given by the expression \(a^{4n}-13\). If the second term of the sequence is \(243\), which of the following is the value of \(a\)?
A right-angled triangle \(ABC\) with the right angle at the vertex \(C\) is given in the picture. Calculate the height \(v_c\), if \(a=20\,\mathrm{cm}\) and \(\beta=50^{\circ}\).
A right-angled triangle \(ABC\) with the right angle at the vertex \(C\) is given in the picture. Calculate the length of the side \(b\), if \(a=20\,\mathrm{cm}\) and \(\beta=34^{\circ}\).
A right-angled triangle \(ABC\) is given in the picture. Its hypotenuse is \(10\,\mathrm{cm}\) long and the measure of its internal angle \(\alpha\) is \(30^{\circ}\). What are the lengths of the legs in the triangle?
A right-angled triangle \(ABC\) with the right angle at the vertex \(C\) is given in the picture. The length of the side \(c\) is \(5\,\mathrm{cm}\) and the measure of the angle \(\alpha\) is \(35^{\circ}\). What is the length of the side \(a\)?
We cut two triangles from the rectangular plate so that the resulting trapezoid has an area of \(30\,\mathrm{cm}^2\). One of its bases is twice as long as the other. What is the area of the two triangles that are cut off?