The Pythagorean Theorem can be used to find the missing side length of a triangle when two other side lengths are known. Consider the following measurements. a =\( 20 \) \( b = \) ? \( c = 29 \) Use the formula \( c = \sqrt { a ^ { 2 } + b ^ { 2 } } \) , a modified version of the Pythagorean Theorem, to find the missing side length, \( b \) . What is the value of \( b \) ? \( 441 \) \( 21 \) \( 35.2 \) \( 840.8\) 

Find the area of the sector of a at the centre is \( 140^{\circ} \). (Take \( \pi= \) Solution Area A of a sector is given by; \( \begin{aligned} \text { A }=\frac{\theta}{360} \times \pi r^{2}\end{aligned} \) \( \begin{aligned} \therefore \text { Area } & =\frac{140}{360} \times \frac{22}{7} \times 3^{2} \\ & =11 \mathrm{~cm}^{2}\end{aligned} \)

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

3 треугольнике \( A B C \) к стороне \( A B=9 \) см опущена высота, длина которой составила 8 см Найди площадь этого треугольника и дай ответ з квадратных сантиметрах.

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