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olasank [31]
3 years ago
13

30 points to anyone who solves this

Mathematics
1 answer:
shtirl [24]3 years ago
8 0

Answer:

Step-by-step explanation:

cos R = adj/hyp

R = cos⁻¹(9/10) = 25.8419327... ≈ 25.8°

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Given: △ABC, E∈ AB m∠ABC=m∠ACE AB=34, AC=20 Find: AE
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AE = 11.76 units

Step-by-step explanation:

For better understanding of the solution, see the attached figure :

Given : E ∈ AB, m∠ABC = m∠ACE, AB = 34 and AC = 20

To find AE :

In ΔABC and ΔACE,

m∠ABC = m∠ACE ( Given )

∠A = ∠A    ( Common angle for both the triangles )

By AA postulate of similarity of triangles, ΔABC ~ ΔACE

So, proportion of the corresponding will be equal.

\implies \frac{AC}{AB}=\frac{CE}{BC}=\frac{AE}{AC}\\\\\implies\frac{AC}{AB}=\frac{AE}{AC}\\\\\implies\frac{20}{34}=\frac{AE}{20}\\\\\implies AE=\frac{20\times 20}{34}\approx 11.76

Hence, AE = 11.76 units

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