Altitude of Triangle II

Submitted by vladimir.arzt on Sat, 10/19/2024 - 12:34

Project ID:

7200000094

Accepted:

SubArea:

Type:

Layout:

Question:

Point

D

(the foot of the altitude

C D

) divides side

c

of triangle

A B C

into two segments of lengths

c_{a}

and

c_{b}

, such that

c = c_{a} + c_{b}

(see the picture). Match each triangle, specified by the lengths of the segments or the side

c

and the size of an inner angle, to the length of its altitude

C D

rounded to two decimal places.

Unfolding Image:

Questions Title:

Triangle

Answers Title:

Lenght of Altitude

C D

Question 1:

\begin{aligned} c_{a} & = 3 \\ c_{b} & = 5 \\ β & = 35^{\circ} \end{aligned}

Answer 1:

3.5

Question 2:

\begin{aligned} c_{a} & = 2.5 \\ c_{b} & = 6.1 \\ β & = 40^{\circ} \end{aligned}

Answer 2:

5.12

Question 3:

\begin{aligned} c & = 10.3 \\ c_{b} & = 6.2 \\ α & = 60^{\circ} \end{aligned}

Answer 3:

7.10

Question 4:

\begin{aligned} c_{a} & = 5.4 \\ c_{b} & = 3.7 \\ α & = 45^{\circ} \end{aligned}

Answer 4:

5.4

Question 5:

\begin{aligned} c & = 11.5 \\ c_{b} & = 4.2 \\ β & = 60^{\circ} \end{aligned}

Answer 5:

12.64

Question 6:

\begin{aligned} c & = 11.8 \\ c_{b} & = 3.5 \\ α & = 30^{\circ} \end{aligned}

Answer 6:

4.79

Answer 7:

10.74

Answer 8:

2.1

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