Question

tan net trange (网) and s ta vaue of dn (的)

Explanation:

Step1: Identify the triangle type

This is a right - triangle with right - angle at \(B\), hypotenuse \(FP = 10\) and one leg \(BP=8\). Let the other leg be \(BF\). We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Let \(a = BP = 8\), \(c=FP = 10\) and \(b = BF\).

Step2: Apply the Pythagorean theorem

From \(a^{2}+b^{2}=c^{2}\), we can re - arrange it to find \(b\): \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(a = 8\) and \(c = 10\) into the formula: \(b=\sqrt{10^{2}-8^{2}}=\sqrt{100 - 64}=\sqrt{36}=6\).

Step3: Find the area of the right - triangle

The area of a right - triangle is given by the formula \(A=\frac{1}{2}\times\text{base}\times\text{height}\). Here, the base can be \(BP = 8\) and the height can be \(BF=6\). So \(A=\frac{1}{2}\times8\times6\).

Step4: Calculate the area

\(\frac{1}{2}\times8\times6 = 4\times6=24\).

Answer:

The area of the right - triangle is \(24\) square units.