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2 years ago

In triangle ΔABC, ∠C is a right angle and CD is the altitude to AB . Find the angles in ΔCBD and ΔCAD if: b m∠A=65°

Mathematics

1 answer:

lukranit [14]2 years ago

8 0

Answer:

Step-by-step explanation:

In triangle ΔABC,

<C=90° (Given angle is a right angle).

m∠A=65° (Also given).

The sum of angles of a triangle is 180°.

We can set an equation for angles A, B and C.

<A+<B+<C=180°.

Now we are plugging values of <A and <C in the equation above.

90°+<B+65°=180°

<B+155=180.

Subtract 155 from both sides.

<B+155-155=180-155.

<B=25°.

Therefore, <B=25°.

Now, in triangle ΔCBD.

<D=90°. (Give CD is perpendicular to AB. A perpendicular line subtands an 90° angle.)

<B=25° (We found above).

Now, the sum of the angles of triangle ΔCBD is also 180°.

We can set up another equation,

<B + <D + < BCD = 180 °.

Plugging values of B and D in the equation above.

25+90+<BCD=180.

115+<BCD=180.

Subtract 115 from both sides.

115+<BCD-115=180-115.

<BCD=65°.

Now, in triangle ΔCAD.

<D = 90°.

<A = 65°

We need to find <ACD.

Now, the sum of the angles of triangle ΔCAD is also 180 degrees.

We can set up another equation,

<A+<D+<ACD=180°.

65+90+<ACD=180.

155+<ACD=180.

Subtract 155 from both sides.

<ACD+155-155=180-155.

<ACD=25°.

Therefore, <ACD=25°, <BCD=65°, <D=90°, <B=25°.

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A rectangle that had the perimeter of 70 and the area of 250 has enlarged; its sides became twice as long. what is the new area

aliya0001 [1]

The perimeter of the original rectangle is:
P = 2w + 2l = 70
The area of the original rectangle is:
A = w * l = 250
Then, by modifying the length of its sides we have:
Perimeter:
P '= 2 (2w) +2 (2l)
Rewriting:
P '= 2 (2w + 2l)
P '= 2P
P '= 2 (70)
P '= 140
Area:
A '= (2w) * (2l)
Rewriting:
A '= (2) * (2) (w) * (l)
A '= 4 * w * l
A '= 4 * A
A '= 4 * 250
A '= 1000
Answer:
the new area and the new perimeter are:
P '= 140
A '= 1000

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2 years ago

my class collected 389 milk jugs. We used 40 jugs. We gave 30 milk to the first graders. how many milk jugs did we have?

BartSMP [9]

We will just do the following steps:-

389 - 40 = 349
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Hope I helped ya!!

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2 years ago

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Artyom0805 [142]

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1 year ago

A certain temperature measurement is performed 500 times. The mean value is 0 deg F and the standard deviation is 1 deg F. Assum

egoroff_w [7]

Answer:

477

Step-by-step explanation:

Given that:

Number of trials (n) = 500

Mean (m) = 0

Standard deviation (s) = 1

how many readings fall within +/- 2.000 deg F of the mean value

Mean of 0 and standard deviation of 1

P(-2 ≤ x ≤ 2)

Using the Z probability calculator :

P(x ≤ 2) = 0.97725 ;

P(x ≤ - 2) = 0.02275

Hence :

P(x ≤ 2) - P(x ≤ - 2) = 0.97725 - 0.02275 = 0.9545

Hence, number of readings in 500 trials:

0.9545 * 500 = 477.25

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1 year ago

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.

seraphim [82]

Keywords:

Quadratic equation, vertex shape, parabola

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