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2 years ago

Given PA=13 in. and CB=15 in. What is CA ?

Mathematics

2 answers:

alexandr1967 [171]2 years ago

8 0

Triangles CPA and CPB are both right triangles. They share a leg, so that leg in one triangle is congruent to that leg in the other triangle. We are given that PA is congruent to PB by the hash marks on the diagram. Thus two legs and an included angle are congruent between the triangles.

... ∆CPA ≅ ∆CPB by the SAS postulate

Then side CA ≅ CB = 15 in, because corresponding parts of congruent triangles are congruent (CPCTC).

... CA is 15 in.

Ratling [72]2 years ago

6 0

Since CB and CA are congruent. CA is 15 in.

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Zinaida [17]

16 ft

Explanation

Step 1

because the ligth comes in the same angle, we have 2 similar triangles .

so,as the triangles are similar,the ratio of the shorter leg to the bigger leg must be equal.

$\begin{gathered} ratio=\frac{shorter\text{ leg}}{\text{bigger leg}} \\ ratio1=ratio2 \\ \frac{h}{24}=\frac{4}{6} \end{gathered}$

Step 2

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$\begin{gathered} \frac{h}{24}=\frac{4}{6} \\ \text{cross multiply} \\ 6\cdot h=4\cdot24 \\ 6h=96 \\ \text{divide boths} \\ \frac{6h}{6}=\frac{96}{6} \\ h=16 \end{gathered}$

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6 months ago

The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than

svlad2 [7]

The shop sold 36 sundaes and 28 banana spilts

Solution:

Let "a" be the number of sundaes sold

Let "b" be the number of banana spilts sold

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On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156

Therefore,

Number of sundaes sold = 8 + number of banana spilts sold

a = 8 + b ------- eqn 1

Also, given that they made $ 156

Therefore, we frame a equation as:

Number of sundaes sold x Cost of 1 sundaes + number of banana spilts sold x Cost of 1 banana spilt = 156

$a \times 2+b \times 3 = 156$

2a + 3b = 156 ---------- eqn 2

Substitute eqn 1 into eqn 2

2(8 + b) + 3b = 156

16 + 2b + 3b = 156

16 + 5b = 156

5b = 156 - 16

5b = 140

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