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eimsori [14]
4 years ago
14

In triangle ΔABC, ∠C is a right angle and CD is the height to AB. Find the angles in ΔCBD and ΔCAD if:

Mathematics
1 answer:
Lostsunrise [7]4 years ago
7 0

Answer:

m\angle CDB=90°

m\angle CBD=90- \alpha°

m\angle BCD=\alpha°

m\angle CDA=90°

m\angle CAD=\alpha°

m\angle ACD=90- \alpha°

Step-by-step explanation:

The triangles are drawn below.

Since, CD is the height to AB, therefore, CD is perpendicular to AB.

Therefore, angles m\angle CDA=m\angle CDB=90°

Also, m\angle CAD is same as m\angle A.

Therefore, m\angle CAD=\alpha°

Now, triangles ΔCBD and ΔCAD are right angled triangles.

So, for the right angled triangle ΔCAD,

m\angle CAD+m\angle ACD=90\\\alpha + m\angle ACD=90\\m\angle ACD=90- \alpha

Now, from the figure,

m\angle C=m\angle ACD+m\angle BCD\\90=90- \alpha + m\angle BCD\\\therefore m\angle BCD=\alpha

From \DeltaCBD,

m\angle BCD+m\angle CBD=90\\\alpha + m\angle CBD=90\\m\angle CBD=90- \alpha

Hence, all the angles of the triangles ΔCBD and ΔCAD are:

m\angle CDB=90°

m\angle CBD=90- \alpha°

m\angle BCD=\alpha°

m\angle CDA=90°

m\angle CAD=\alpha°

m\angle ACD=90- \alpha°

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Nick and June win some money and share it in the ratio 4:5. Nick gets £40. How much did June get?
sineoko [7]

Answer:

June gets \£50

Step-by-step explanation:

Let

x ----> amount of money Nick gets

y ----> amount of money June gets

we know that

\frac{x}{y}=\frac{4}{5} -----> equation A

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solve the system by substitution

substitute equation B in equation A

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y=\£50

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4 years ago
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dalvyx [7]

Answer:

1. Congruent

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3 years ago
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Gawd that looks really hard
6 0
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against the wind a small plane flew 280 miles in 1 hour and 10 minutes. the return trip took only 50 minutes. What was the speed
Amanda [17]
1)  1hour 10minutes = \frac{7}{6} hours,
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Answer: speed of wind is 48 miles/hours, speed of  </span>plane in still air is 288 miles/hours



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3 0
3 years ago
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