Given:
We have the two triangles:
ABC and ADC
Where:
AB = 10
AC = 8
Let's solve for the following:
• (a). Write a similiarity statement for the two similar triangles.
Two triangles are similar if their corresponding sides are in proportion.
To write a siiliarity statement, we have:
ΔABC ~ ΔADC
• (b). Let's find the length of BC.
To solve for BC, since ABC is a right traingle, apply Pythagorean Theorem:
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ \\ BC^2=AB^2-AC^2 \\ \end{gathered}[/tex]
Where:
AB = 10
AC = 8
Thus, we have:
[tex]\begin{gathered} BC^2=10^2-8^2 \\ \\ BC^2=100-64 \\ \\ BC^2=36 \\ \\ BC=\sqrt{36} \\ \\ BC=6 \end{gathered}[/tex]
• (c). Let's find the length of CD.
Since they are similar triangles, the corresponding angles will be equal.
Thus, angle D = angle B = 36 degrees.
Now, apply the trigonometric ratio for tangent:
[tex]tan\theta=\frac{opposite}{adjacent}[/tex]
Where:
Opposite side = AC = 8 units
Adjcaent side = CD
Hence, we have:
[tex]\begin{gathered} tan36=\frac{8}{CD} \\ \\ CD=\frac{8}{tan36} \\ \\ CD=\frac{8}{0.72654} \\ \\ CD=11 \end{gathered}[/tex]
Therefore, the length of CD is 11 units.
ANSWER:
• (A). ,ΔABC, ~ ,ΔADC
• (B). 6 units
• (C). 11 units
