Right angle \( A B C \) is taken by a dilation with center \( P \) and scale factor \( \frac{1}{2} \) to angle \( A^{\prime} B^{\prime} C^{\prime} \). What is the measure of angle \( A^{\prime} B^{\prime} C \) ? degrees (Lesson 3-4)

\( =11 \mathrm{~cm}^{2} \) Example 2 The area of a sector of a circle is 38.5 cm if the angle subtended at the centre is 90

4. \( A B C \) үшбұрышында \( B C \) биссектрисасы сызылған, \( A K=4 \) см және \( K S=5 \mathrm{~cm} A B C \) үшбұрышының периметрі 36 см AB және BC қабырғаларын табыңыз.

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

5. A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

12-variant 1. \( A(4 ; 3 ;-2), B(-3 ;-1 ; 4), C(2 ; 2 ; 1\} ; \) \( a=\overrightarrow{A B}, b=\overrightarrow{A C}, c=\overrightarrow{C B}, d=2 c-5 b, \quad l=C B, \alpha=4, \beta=3 \)