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Alenkasestr [34]
3 years ago
9

A, b and c are the sides of a right triangle, where side a is across from angle a, side b is across from angle b, and side c is

across from the right angle. if a=19 and b=34∘, find the missing sides and angles in this right triangle
Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
8 0
<span>Find missing length :
</span>
a² + b² = c²
c² = 19² + 34²
c² = 1517
c = √1517
c = 38.95 units.


Find missing angle A:

\dfrac{a}{\sin(a)} =  \dfrac{c}{\sin(c)}

\dfrac{19}{\sin(a)} =  \dfrac{38.95}{\sin(90)}

\sin(a) = 0.488

a = sin^{-1} (0.488)

a = 29.2 \textdegree


Find Missing B:

\dfrac{b}{\sin(b)} = \dfrac{c}{\sin(c)}

\dfrac{34}{\sin(b)} = \dfrac{38.95}{\sin(90)}

\sin(b) = 0.873

b = sin^{-1}(0.873)

b = 60.8 \textdegree


Answer: Missing length =  38.95 units ; Missing angles =  29.2°  and  60.8° 

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(28 + h + p)/4 = k

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Step 2: Solve for <em>k</em>

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3 years ago
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Answer:

CE = 17

Step-by-step explanation:

∵ m∠D = 90

∵ DK ⊥ CE

∴ m∠KDE = m∠KCD⇒Complement angles to angle CDK

In the two Δ KDE and KCD:

∵ m∠KDE = m∠KCD

∵ m∠DKE = m∠CKD

∵ DK is a common side

∴ Δ KDE is similar to ΔKCD

∴ \frac{KD}{KC}=\frac{DE}{CD}=\frac{KE}{KD}

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∴ \frac{KD}{KC}=\frac{5}{3}

∴ KD = 5/3 KC

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∴ KE = 8 + 4.5 = 12.5

∴ CE = 12.5 + 4.5 = 17

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3 years ago
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