a right triangle has one angle that measure 23°. the adjacent leg measures 27.6 cm and the hypotenuse…

a right triangle has one angle that measure 23°. the adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. what is the approximate area of the triangle? round to the nearest tenth. area of a triangle = $\frac{1}{2}bh$ 68.7 cm² 161.8 cm² 381.3 cm² 450.0 cm²

a right triangle has one angle that measure 23°. the adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. what is the approximate area of the triangle? round to the nearest tenth. area of a triangle = $\frac{1}{2}bh$ 68.7 cm² 161.8 cm² 381.3 cm² 450.0 cm²

Answer

Explanation:

Step1: Find the opposite - leg length

We can use the Pythagorean theorem (a^{2}+b^{2}=c^{2}), where (c = 30) (hypotenuse) and (a = 27.6) (adjacent - leg). Let the opposite - leg be (b). Then (b=\sqrt{c^{2}-a^{2}}=\sqrt{30^{2}-27.6^{2}}=\sqrt{(30 + 27.6)(30 - 27.6)}=\sqrt{57.6\times2.4}=\sqrt{138.24}\approx11.76).

Step2: Calculate the area of the triangle

The area formula of a triangle is (A=\frac{1}{2}bh). Here, we can take the adjacent leg as the base (b = 27.6) and the opposite leg as the height (h\approx11.76). So (A=\frac{1}{2}\times27.6\times11.76 = 13.8\times11.76=162.288\approx161.8\mathrm{cm}^{2}).

Answer:

161.8 (cm^{2})