Answer :
Answer:
1. H = 29 cm
2. θ = 44°
Step-by-step explanation:
1. We can find the height of the triangle by considering the isosceles triangle as two right triangles. The height can be found by using Pitagoras:
[tex] L^{2} = H^{2} + B^{2} [/tex]
Where:
L: is the sides of the isosceles triangle = 42 cm
B: is the base = 30 cm
H: is the height =?
Then, the height is:
[tex] H = \sqrt{L^{2} - B^{2}} = \sqrt{(42 cm)^{2} - (30 cm)^{2}} = 29.4 cm = 29 cm [/tex]
2. The two equal angles (θ) can be found using the following trigonometric identity:
[tex] cos(\theta) = \frac{B}{L} [/tex]
[tex] \theta = cos^{-1}(\frac{30 cm}{42 cm}) = 44.4^{\circ} = 44^{\circ} [/tex]
Hence, the two equal angles are 44°.
I hope it helps you!